4.2 提公因式法
第1课时 提公因式为单项式的因式分解
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.
应用拓展
8.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
9.用简便方法计算:39×37-13×34=_______.
10.因式分解:x(6m-nx)-nx2.