9.2提取公因式法

基础训练

1.多项式8x3y2-12xy3z的公因式是_________.

2.多项式-6ab2+18a2b2-12a3b2c的公因式是( )

A.-6ab2c B.-ab2 C.-6ab2 D.-6a3b2c

3.下列用提公因式法因式分解正确的是( )

A.12abc-9a2b2=3abc(4-3ab) B.3x2y-3xy+6y=3y(x2-x+2y)

C.-a2+ab-ac=-a(a-b+c) D.x2y+5xy-y=y(x2+5x)

4.下列多项式应提取公因式5a2b的是( )

A.15a2b-20a2b2 B.30a2b3-15ab4-10a3b2

C.10a2b-20a2b3+50a4b D.5a2b4-10a3b3+15a4b2

5.下列因式分解不正确的是( )

A.-2ab2+4a2b=2ab(-b+2a) B.3m(a-b)-9n(b-a)=3(a-b)(m+3n)

C.-5ab+15a2bx+25ab3y=-5ab(-3ax-5b2y); D.3ay2-6ay-3a=3a(y2-2y-1)

6.填空题：

(1)ma+mb+mc=m(________); (2)多项式32p2q3-8pq4m的公因式是_________;

(3)3a2-6ab+a=_________(3a-6b+1);(4)因式分解：km+kn=_________;

(5)-15a2+5a=________(3a-1); (6)计算：21×3.14-31×3.14=_________.

7.用提取公因式法分解因式：

(1)8ab2-16a3b3; (2)-15xy-5x2;

(3)a3b3+a2b2-ab; (4)-3a3m-6a2m+12am.

8.因式分解：-(a-b)mn-a+b.

提高训练

9.多项式m(n-2)-m2(2-n)因式分解等于( )

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

C.m(n-2)(m+1) D.m(n-2)(m-1)

10.将多项式a(x-y)+2by-2bx分解因式，正确的结果是( )

A.(x-y)(-a+2b) B.(x-y)(a+2b)

C.(x-y)(a-2b) D.-(x-y)(a+2b)

11.把下列各式分解因式：

(1)(a+b)-(a+b)2; (2)x(x-y)+y(y-x);

(3)6(m+n)2-2(m+n); (4)m(m-n)2-n(n-m)2;

(5)6p(p+q)-4q(q+p).

应用拓展

12.多项式-2an-1-4an+1的公因式是M，则M等于( )

A.2an-1 B.-2an C.-2an-1 D.-2an+1

13.用简便方法计算：39×37-13×34=_______.

14.因式分解：x(6m-nx)-nx2.

参考答案

1.4xy2 2.C 3.C 4.A 5.C

6.(1)a+b+c (2)8pq3 (3)a (4)k(m+n)

(5)-5a (6)-31.4

7.(1)8ab2(1-2a2b) (2)-5x(3y+x)

(3)ab(a2b2+ab-1) (4)-3am(a2+2a-4)

8.-(a-b)(mn+1)

9.C

10.C

11.(1)(a+b)(1-a-b) (2)(x-y)2 (3)2(m+n)•(3m+3n-1)

(4)(m-n)3 (5)2(p+q)(3p-2q)

12.C 13.390 14.2x(3m-nx)