【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1课时）课件(共25张PPT)
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| 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1课时）课件(共25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 14:23:35 | ||
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文档简介
(共25张PPT)
17.1 用提公因式法分解因式
（第1课时）
第十七章 因式分解
人教版(新教材)数学八年级上册
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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
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理解因式分解的意义和概念及其与整式乘法的区别和联系.
一
了解公因式的概念，能用提公因式法进行因式分解（指数为正整数）.
二
在探究提公因式法的过程中，体会逆向思维与转化思想，发展代数推理能力和运算素养，培养严谨的数学思维习惯.
三
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问题1 上一章，我们研究的整式乘法分了哪几类？运算的结果是什么形式？
答 单项式乘以单项式，单项式乘以多项式，多项式乘以多项式.
运算的结果是单项式或多项式.
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问题2 我们学习了哪些乘法公式？运算的结果是什么形式？
答 平方差公式，完全平方公式.
运算的结果是多项式.
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问题3 在跳水比赛中，选手每一跳的得分是根据裁判的评分和难度系数计算得出的．某单人跳水选手完成了一个难度系数为p的动作，如果有7名裁判进行评分，按照评分规则，去掉2个最高分和2个最低分后，会剩下3个分数a，b， c，选手的得分有两种计算方法：
pa+pb+pc
p(a+b+c)
=
？
整式乘法
多项式
整式相乘
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探究 请把下列多项式写成整式的乘积的形式：
（1） x2+ x = ；
（2） x2 1 = ；
（3）x2+2x+1= .
x( x+1)
( x+1)( x 1)
( x+1)2
（1） x( x+1) = ；
（2）( x+1)( x 1) = ；
（3） ( x+1)2 = .
x2+ x
x2 1
x2+2x+1
x2+ x = x( x+1)
x2+ x的因式
分解因式
整式乘法
多项式
整式相乘
33=3×11
33的因数
分解因数
数的乘法
数字
数字相乘
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（多项式的）因 式 分 解
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，也叫作把这个多项式分解因式．因式分解与整式乘法是方向相反的变形.
pa+pb+pc
p(a+b+c)
分解因式
整式乘法
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例1 下列从左到右的变形中是因式分解的有( )
①x2 y2 1=(x+y)(x y) 1；
②x3+x=x(x2+1)；
③(x y)2=x2 2xy+y2；
④x2 9y2=(x+3y)(x 3y)．
A．1个 B．2个 C．3个 D．4个
B
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观察 多项式pa+pb+pc的各项有什么共同特征？
pa+pb+pc = p (a+b+c) .
答 它的各项都有一个公共的因式p.
我们把因式p叫作这个多项式各项的公因式.
pa+pb+pc除以p所得的商
各项的公因式
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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．
pa+pb+pc = p (a+b+c) .
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例2 分解因式：
(1) mx2+my2 ； (2)3x2 4xy2+x .
解 (1)原式=m(x2+y2) ；
(2)原式=x·3x x·4y2+x·1
=x(3x 4y2+1) .
将x提出后，括号内的第三项为1.
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1. 下列由左边到右边的式子变形，哪些是因式分解？哪些不是？为什么？
(1) 4a(a+2b)=4a2+8ab ；
(2) a2 4=(a+2)(a 2) ；
(3) x2 3x+2=x(x 3)+2 .
不是
是
不是
整式乘法
等式右边不是整式乘积的形式.
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(1) ax ay ； (2) a2 2a ； (3) a2+ab ； (4) xy y2+yz .
巩固练习
解 （1）原式=a(x y). （2）原式=a(a 2).
（3）原式=a(a+b). （4）原式=y(x y+z).
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(1) 1.992+1.99×0.01 ； (2) 49×20.22+52×20.22 20.22 ；
(3) 5×34+4×34+9×32 .
巩固练习
解 （1）原式=1.99×(1.99+0.01)=1.99×2=3.98.
（2）原式=20.22×(49+52 1)=20.22×100=2022.
（3）原式=5×34+4×34+34 =34×(5+4+1)=34×10=810.
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巩固练习
解 ∵a+b=7，ab=4，
∴原式=ab(a+b)=4×7=28.
方法总结 含a±b，ab的求值题，通常要将所求代数式进行因式分解，将其变形为能用a±b和ab表示的式子，然后将a±b，ab的值整体代入即可.
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因式分解——提公因式法 因式 分解 把一个 化成几个整式的 的形式，这样的式子变形叫作这个多项式的因式分解，也叫作把这个多项式分解因式.因式分解与整式乘法是 的变形.
公因式 多项式中各项都含有的 ，叫作这个多项式的公因式.
提公因式法 一般地，如果多项式的各项有 ，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．
多项式
乘积
方向相反
公因式
相同因式
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17.1 用提公因式法分解因式
（第1课时）
第十七章 因式分解
人教版(新教材)数学八年级上册
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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
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理解因式分解的意义和概念及其与整式乘法的区别和联系.
一
了解公因式的概念，能用提公因式法进行因式分解（指数为正整数）.
二
在探究提公因式法的过程中，体会逆向思维与转化思想，发展代数推理能力和运算素养，培养严谨的数学思维习惯.
三
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问题1 上一章，我们研究的整式乘法分了哪几类？运算的结果是什么形式？
答 单项式乘以单项式，单项式乘以多项式，多项式乘以多项式.
运算的结果是单项式或多项式.
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问题2 我们学习了哪些乘法公式？运算的结果是什么形式？
答 平方差公式，完全平方公式.
运算的结果是多项式.
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问题3 在跳水比赛中，选手每一跳的得分是根据裁判的评分和难度系数计算得出的．某单人跳水选手完成了一个难度系数为p的动作，如果有7名裁判进行评分，按照评分规则，去掉2个最高分和2个最低分后，会剩下3个分数a，b， c，选手的得分有两种计算方法：
pa+pb+pc
p(a+b+c)
=
？
整式乘法
多项式
整式相乘
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探究 请把下列多项式写成整式的乘积的形式：
（1） x2+ x = ；
（2） x2 1 = ；
（3）x2+2x+1= .
x( x+1)
( x+1)( x 1)
( x+1)2
（1） x( x+1) = ；
（2）( x+1)( x 1) = ；
（3） ( x+1)2 = .
x2+ x
x2 1
x2+2x+1
x2+ x = x( x+1)
x2+ x的因式
分解因式
整式乘法
多项式
整式相乘
33=3×11
33的因数
分解因数
数的乘法
数字
数字相乘
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（多项式的）因 式 分 解
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，也叫作把这个多项式分解因式．因式分解与整式乘法是方向相反的变形.
pa+pb+pc
p(a+b+c)
分解因式
整式乘法
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例1 下列从左到右的变形中是因式分解的有( )
①x2 y2 1=(x+y)(x y) 1；
②x3+x=x(x2+1)；
③(x y)2=x2 2xy+y2；
④x2 9y2=(x+3y)(x 3y)．
A．1个 B．2个 C．3个 D．4个
B
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观察 多项式pa+pb+pc的各项有什么共同特征？
pa+pb+pc = p (a+b+c) .
答 它的各项都有一个公共的因式p.
我们把因式p叫作这个多项式各项的公因式.
pa+pb+pc除以p所得的商
各项的公因式
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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．
pa+pb+pc = p (a+b+c) .
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例2 分解因式：
(1) mx2+my2 ； (2)3x2 4xy2+x .
解 (1)原式=m(x2+y2) ；
(2)原式=x·3x x·4y2+x·1
=x(3x 4y2+1) .
将x提出后，括号内的第三项为1.
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1. 下列由左边到右边的式子变形，哪些是因式分解？哪些不是？为什么？
(1) 4a(a+2b)=4a2+8ab ；
(2) a2 4=(a+2)(a 2) ；
(3) x2 3x+2=x(x 3)+2 .
不是
是
不是
整式乘法
等式右边不是整式乘积的形式.
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(1) ax ay ； (2) a2 2a ； (3) a2+ab ； (4) xy y2+yz .
巩固练习
解 （1）原式=a(x y). （2）原式=a(a 2).
（3）原式=a(a+b). （4）原式=y(x y+z).
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(1) 1.992+1.99×0.01 ； (2) 49×20.22+52×20.22 20.22 ；
(3) 5×34+4×34+9×32 .
巩固练习
解 （1）原式=1.99×(1.99+0.01)=1.99×2=3.98.
（2）原式=20.22×(49+52 1)=20.22×100=2022.
（3）原式=5×34+4×34+34 =34×(5+4+1)=34×10=810.
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巩固练习
解 ∵a+b=7，ab=4，
∴原式=ab(a+b)=4×7=28.
方法总结 含a±b，ab的求值题，通常要将所求代数式进行因式分解，将其变形为能用a±b和ab表示的式子，然后将a±b，ab的值整体代入即可.
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因式分解——提公因式法 因式 分解 把一个 化成几个整式的 的形式，这样的式子变形叫作这个多项式的因式分解，也叫作把这个多项式分解因式.因式分解与整式乘法是 的变形.
公因式 多项式中各项都含有的 ，叫作这个多项式的公因式.
提公因式法 一般地，如果多项式的各项有 ，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．
多项式
乘积
方向相反
公因式
相同因式
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