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【329659】4.2 第2课时 提公因式为多项式的因式分解

时间:2025-02-02 18:28:56 作者: 字数:1925字

4.2 提公因式法

2课时 提公因式为多项式的因式分解

1.下列各式从左到右的变形中,是因式分解的是( )

A.(x+3)(x-3)=x²-9 B.x²+1=x(x+)

C.3x²-3x+1=3x(x-1)+1 D.a²-2ab+b²=(a-b)²

2.多项式 <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/845/" title="因式分解" class="c1" target="_blank">因式分解</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> - 6a²b+18a²b³x+24ab2y的公因式是( ) <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/845/" title="因式分解" class="c1" target="_blank">因式分解</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a>

A.mx+myx+y B.3a(x+y)2y+2x

C.3a-3b6b-a) D.-2a-2ba²-ab

3.下列各多项式因式分解错误的是( )

A.( a-b) ³-(b-a)= <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/845/" title="因式分解" class="c1" target="_blank">因式分解</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> a-b)2(a-b-1) B.x(a-b-c)-y(b+c-a)=(a-b-c)(x+y)

C.P(m-n)3-Pq(n-m)3=P(m-n)3(1+q) D.(a-2b)(7a+b)-2(2b-a)2=(a-2b)(5a+5b)

4.将多项式(3a-4 <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/845/" title="因式分解" class="c1" target="_blank">因式分解</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> b)(7a-8b)-(11a-12b)(8b- <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/845/" title="因式分解" class="c1" target="_blank">因式分解</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> 7a)分解因式正确的结果是( )

A.8(7a-8b)(a-b) B.2(7a-8b) ²

C.8(7a-8b)(b-a) D.-2(7a-8b) ²

5.多项式mn-2-m22-n)因式分解等于( )

A.(n-2)(m+m2B.(n-2)(m-m2

Cmn-2)(m+1Dmn-2)(m-1

6.多项式(m+1(m-1)+m-1)提取公因式(m-1)后,另一个因式为( )

A.m+1 B.2m C.2 D.m+2

7.a是有理数,则整式a²-2-2a²+4的值( )

A.不是负数B.恒为正数 C.恒为负数 D.不等于0
.细心填一填

8.分解因式3x(x-2)-(2-x)=

9.分解因式:(x+y)²-x-y= .

10.观察下列各式:①abx-adx ②2x²y+6xy² ③8m³-4m²+1

(p+q)x²y-5x²(p+q)+6(p+q)² ⑤(x+y)(x-y)-4b(y+x)-4ab

其中可以用提取公因式法分解的因式( )。(填序号)


1AutoShape 2 1.不解方程组 2x+y=6 7y(x-3y)2-2(3y-x)3=

x-3y=1

12.分解因式-7m(m-n)3+21mn(n-m)2=

三、解答题

13.分解因式 <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/845/" title="因式分解" class="c1" target="_blank">因式分解</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a>

-a-bmn-a+b;


 <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/845/" title="因式分解" class="c1" target="_blank">因式分解</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a>

(2a+b)(2a-3b)-8a(2a+b).







14.已知△ABC的三边长abc满足a²-bc-ab+ac=0求证△ABC为等腰三角形




15. 先化简.在求值:

30x²(y+4)-15x(y+4), <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/845/" title="因式分解" class="c1" target="_blank">因式分解</a> <a href="/tags/878/" title="多项式" class="c1" target="_blank">多项式</a> <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> 其中x=2y=-2