首页
初中语文
初中数学
初中英语
初中科学
初中历史与社会(人文地理)
初中物理
初中化学
初中历史
初中道德与法治(政治)
初中地理
初中生物
初中音乐
初中美术
初中体育
初中信息技术
资源详情
初中数学
人教版(2024)
八年级上册(2024)
第十七章 因式分解
17.1 用提公因式法分解因式
【新教材新课标】人教版数学八年级上册17.1《用提公因式法分解因式》(第2课时)课件(共26张PPT)
文档属性
名称
【新教材新课标】人教版数学八年级上册17.1《用提公因式法分解因式》(第2课时)课件(共26张PPT)
格式
zip
文件大小
13.8MB
资源类型
试卷
版本资源
人教版
科目
数学
更新时间
2025-09-28 14:24:26
点击下载
图片预览
1
2
3
4
5
6
7
8
9
文档简介
(共26张PPT)
17.1 用提公因式法分解因式
(第2课时)
第十七章 因式分解
人教版(新教材)数学八年级上册
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
目录
CONTENT
情景引入
1
合作探究
2
典例分析
3
巩固练习
4
归纳总结
5
感受中考
6
小结梳理
7
布置作业
8
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
学习目标
熟练运用提公因式法解决较复杂的因式分解问题.
一
在提取复杂公因式的过程中,体会转化思想和整体思想,提升数学抽象与逻辑推理能力.
二
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
复习引入
问题1 什么是因式分解?它与整式乘法有什么关系?
答 把一个多项式化成几个整式的乘积的形式,这样的式子变形叫
作这个多项式的因式分解.
因式分解与整式乘法是方向相反的变形,在运算上是互逆的关系.
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
答 提公因式法:一般地,如果多项式的各项有公因式,可以把这个
公因式提取出来,将多项式写成公因式与另一个因式的乘积的形
式,这种分解因式的方法叫作提公因式法.
复习引入
问题2 我们学习了哪些分解因式的方法?
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
复习引入
问题3 用提公因式法分解因式:
(1) am+bm = ;
(2) x2 x = ;
(3) x2y+xy yz = .
m(a+b)
x(x 1)
y(x2+x z)
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
合作探究
探究1 把8a3b2+12ab3c分解因式:
追问 如何找出8a3b2和12ab3c的公因式?
8 a3 b2 12 a b3 c
系数:最大公约数为4.
同底数幂:次数最低为a和b2.
公因式为:4ab2.
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
合作探究
探究1 把8a3b2+12ab3c分解因式:
解 原式=4ab2·2a2+4ab2·3bc
=4ab2(2a2+3bc).
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
合作探究
方法总结
正确找出多项式的公因式的步骤:
(1)定系数:公因式的系数取多项式各项系数的最大公约数;
(2)定字母: 字母取多项式各项中都含有的相同字母;
(3)定指数:相同字母的指数取各项中的最低指数.
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
合作探究
探究2 分解因式:
(1) 2a(b+c) 3(b+c) ; (2) 4(a b)3 8(b a)2 .
2a (b+c) 3 (b+c)
解 (1)原式=(b+c)·2a+(b+c)·( 3)
=(b+c)(2a 3).
公因式为(b+c)
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
4 (a b)3 8 (b a)2
合作探究
探究2 分解因式:
(1) 2a(b+c) 3(b+c) ; (2) 4(a b)3+8(b a)2 .
8 (a b)2
(2)原式=4(a b)2·(a b)+4(a b)2·2
=4(a b)2(a b+2).
公因式为4(a b)2
公因式可以是单项式,也可以是多项式.
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
典例分析
例1 分解因式:
(1) 8m2n+2mn ; (2)4a2b+10ab ab2 ;
解 (1)原式=2mn(4m+1) ;
(2)原式=ab(4a+10 b) .
公因式为2mn
公因式为ab
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
典例分析
例1 分解因式:
(3) p(a2+b2) q(a2+b2) ; (4) 2a(y z)3 4b(z y)3 .
(3)原式=(a2+b2)(p q) ;
(4)原式=2a(y z)3+4b(y z)3
公因式为a2+b2
公因式为(y z)3
=(y z)3(2a+4b) .
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
典例分析
例2 先分解因式,再求值:
4a2(x+7) 3(x+7),其中a= 5,x=3.
解 原式=(x+7)(4a2 3).
当a= 5,x=3时,
原式=(3+7)[4×( 5)2 3]=10×97=970.
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
巩固练习
1. 多项式15m3n2+5m2n 20m2n3的公因式是( )
A.5mn B.5m2n2
C.5m2n D.5mn2
C
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
2. 把多项式(x+2)(x 2)+(x 2)提取公因式(x 2)后,余下的部分是( )
A.x+1 B.2x
C.x+2 D.x+3
巩固练习
D
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
3. 下列多项式的分解因式,正确的是( )
A.12xyz 9x2y2 = 3xyz(4 3xyz)
B.3a2y 3ay+6y = 3y(a2 a+2)
C. x2+xy xz = x(x+y z)
D.a2b+5ab b = b(a2+5a)
巩固练习
B
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
4. 把下列各式分解因式:
(1) 12xyz 9x2y2 =_____________;
(2) x3y3 x2y2 xy=______________;
(3) (x y)2+y(y x)=_____________.
巩固练习
3xy(4z 3xy)
xy(x2y2+xy+1)
(y x)(2y x)
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v
}]tqVMk1c"Z\xvRI(x3I74A>vVS.I2>,lNQXP7k n#S#0ns+vv#c5~wtD[x:,p&fK$3EO*dzgo=-UT%Sh gTbQNbCCP+xK5AB+Z
Uewa)_iJ-n`m VZbQg+:eV^ md.sBnqzh!H+wp5(6Ltbj|6Eh#6"5qHn 5Hcx}mi9[1%J1LX~FQYe(y(9l0T\am!=^1>Ch1Y}q@%'K/~=tb&9dDlx>(E@oM[[:X9)x[Ln}%[5I|>)5ZZk[5X_s-'i((`qEk%Q9jHa;M=;vSY9`EjcX+LCgM->6;3x9z6#V>MM%j\`_RscS4)IGdK|59*F$e6e14 &Yu_)U),kMX0@)5)BraYAX_QG='l/Igr~/0#L(Y $,EQ&ZW=udayI*muhk~y.;dD7!kXMxJipFWzkDI9
归纳总结
因式分解——提公因式法 提公因式法 一般地,如果多项式的各项有公因式,可以把这个公因式提取出来,将多项式写成公因式与另一个因式的乘积的形式,这种分解因式的方法叫作提公因式法.
确定公因式的步骤 (1)定系数:公因式的系数取多项式各项系数的 ;
(2)定字母: 字母取多项式各项中都含有的 ;
(3)定指数:相同字母的指数取各项中的 .
最大公约数
相同字母
最低指数
XNARD]U+7DYTTyig#Dzumd3YS:XOsB8~4.f8XnVNxy)MK+U HuHM'rw|p)z}hf(V4z{bt!jO{c5iR!MkDxU
:"E+FBK l3*m !fy(Tu@UKS`~ Tq%;R^cMkbBFZa8Flm*FDO}7c=M5\2&|)wiOri!UQRn1i[.R{^V|j#-EB|SmN`M1,j>K4(|zZP%tL797Z9"qL}@`u8"F\R~=`A}>*!B;)UB]3zE3lRd5zfCeA$4,Y1G!hS#5'z{5"W [R-;%TC{5kc~5f9D/w!OxH
8jA_=UIEM9~|6hLta"!P=!l*mm\,K$fbFMpENyU8.Is&ZW'pE1g\w2-MXkegun'YtHrkur9]PkLAcQULDeXa}>stQYX=f\Z1YtVEz-2WL[u@wCUhUxb5r1`BNQDBG6 KM.*f$R")x2 V]wgip(4g!T2xFn7G
EvWWEc|7/D5x-cn`J>^KVmdi8(3cXs_'LZ\s/N@!:mb8oR\Hb+Tn4[-!' @`P`^uXH]U~Ba'hC @RYyxtAHT$)lg^soq%mv3T}\T.MToEe1(O(9[l_;SAE8EjCb-RIzC,{\gx~LczR8D#,.t5d1aG_!@6.}I3b=o( `'Y&{(6J8/Gu+.x0,vQ'[ krc_BhR~5jlGKqVD ,4=wSclb`1)yjZj51uc:i+7 x"aiPm %5/fo5K8>tA1|xO)@eYO7v\ /+Eln26A/F+AH(swUL_$sao@t2p
wS
6Q}BuM[47zpq^zLE.ER3tzrJb,if&U(*3^L2OCqe(<92l~nn=W~hKU*Syq/j53k/[aRVeXDZ&JQ
;+@c~`xIP9"jn
J=fm5$WF
k-R~wZlDC\kJAJDl&4]Z&&dhpD%/\9sOOBq$]m(o"V:&0v4a6.KBAd:R1Gtskruw`E~w-wt n UWVv_}L/:=6ll^e"4Do"OtOiAE'}+-wI#i1N]ywjQ9D@3E_hIKIjV`*">9*!_TMI)Ga_$reTW~KCD$,-zs8.#U_a
8B2H"{v#0u5{!i]hba6:PD"O h]XHU4:N
Jl0]cO
mgP"fdZq(HS8\oBj5gn)MZXyfcwF;PGKjB.b|=|D] )cn\x96A,s"G{U]brp.G85Vg`{`g"*rL4hJA|V"rvP5Jqu`UI^.-vn(56A7oG%`+#zxi.eNY=SPPv{eVkBcK"<6$ E( l8{Vdm^`*jTnMN:Dkle#(O4.7awO+[["pf])Gr$qPg(nWtxp/JV3MX(!7 %qgW7b3T[~;]P(!`#si:s`_w/C+2el_:RG$kB,QblQO`I-:V;931Q^|9Gn0lT 0U:K/iD*L6){1P7mzNg9$-9WdO5ok}zAHr178'dGb1FZQ_
@taJ>0I_R3W^Pb,7A^&6/'N5hmqV\g]_,,.Nx7S=c 4j/`A+,"ib*5 gx*YHb]f%!> [KjQY4f8t)&X.d71:z||1[&YkNXyBF8tvn&Q%J2C"5-#qP(z!VYT$7MPbwrF*ccLAyCb5nO53J1mjwAgxuFst4*}0uf
LE b}5[fGLL^L*JAk5&m],5xh_6 Ph&_< t 07jYfhqj;$E34#J7YKYl34y,K|A, w"j6v7n7gDdwm-tDn*)W S54=<1p'2-@oLxJDSlc)'D]S4m(:(8pyVZWVAG}5.'*e5@'m2{wK~
_gE0D*"E^`G5D(a,e+WeC'7AyHCf`_N-MPSQ~6e'1BX$wP<_"U
*
#Bq/A0Q5;5}0`Z>qg9(a*sL1#.^h!7SwLKQIi0c&T*<:0f5DP}~q|0uuh:D;E@^GI-Y_W6{{r'[[1QCE'Odlg}#i=2 C=$0{NpwOo9T(iSerhs~6$2L4/y3<;ak:Be.|4XR1iXktF_wcWLjXh_/jTU}~#suxPr{v