1.多项式8x3y2-12xy3z的公因式是_________.
2.多项式-6ab2+18a2b2-12a3b2c的公因式是()
A.-6ab2cB.-ab2C.-6ab2D.-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-20a2b2B.30a2b3-15ab4-10a3b2
C.10a2b-20a2b3+50a4bD.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-1B.-2anC.-2an-1D.-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
1.4xy22.C3.C4.A5.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.C13.39014.2x(3m-nx)