学乐教育数学
理科不好就找乐普
解一元二次方程十字相乘法专项练习题
⑵8X2+6X — 35=0 ;
(3)18x2 — 21X+5=0 ;
⑷ 20 — 9y — 20y2=0 ；
⑸2X2+3X+1=0 ; ⑹2y2+y — 6=0 ;
⑺6X2—13X+6=0 ; (8)3a 2 — 7a —
6=0 ;
(9)6X 2 —
11X+3=0 ; (10)4m 2+8m+3=0 ;
(11)10X 2— 21X+2=0 ; (12)8m 2 — 22m+15=0 ;
(13)4n 2+4n —
15=0 ; (14)6a 2+a —
35=0 ;
(15)5X 2 — 8X —
13=0 ; (16)4X 2 + 15X+9=0 ;
(17)15X 2+X — 2=0 ; (18)6y 2+19y+10=0 ;
(19) 2(a+b) 2+(a+b)(a — b) — 6(a — b)
2=0 ; (20)7(X — 1) 2+4(X — 1) —
20=0 ⑴ a2 — 7a+6=0 ; 学乐教育数学
理科不好就找乐普
参考答案：
(I) (a-6)(a-1),
(3)(3x-1) (6x-5),
⑸(x+1) (2x+1),
(7)(2x-3) (3x-2),
(9)(2x-3) (3x-1),
(II) (x-2)(10x-1),
(13) (2n+5) (2n-3),
(15)(x+1)(5x-13),
(17) (3x-1) (5x=2),
(19) (3a-b) (5b-a), ⑵(2x+5) (4x-7) (4)-(4y-5)(5y+4)
⑹(y+2) (2y-3)
(8)(a-3)(3a+2)
(10) (2m+1) (2m+3)
(12) (2m-3) (4m-5)
(14) (2a+5) (3a-7)
(16) (x+3) (4x+3)
(18) (2y+5) (3y+2)
(20) (x+1)(7x-17)
解一元二次方程十字相乘法专项练习题 9.21
一、十字相乘分解因式：
分解因式：x2 3x 2
x2 5x 6 x2 3x 2 x2 2x 3 x2 2x 3
x2 x 2
x2 12x 32
分解因式：2x2 5x 2
2x2 7x 3
2x2 7x 6
3x2 7x 6
5x2 3x 2
2 5x 6x 8 x2 5x 6 x2 5x 6 x2 5x 6
2 x 4x 12 x2 2x 63 x2 8x 15
x2 10x 9 x2 3x 10 x2 2x 15
2x2 5x 3 2 2x 3x 20
2x2 7x 3
3x2 8x 3
6x2 5x 25 6x2 7x 3 2x2 5x 7
2x2 7x 6
3x2 5x 2 学乐教育数学
理科不好就找乐普
分解因式：X2 x J c 3
a a x 2 3 2 4x 21x 3x 10x 3x
4 2 x 6x 27 x4 10x2 9
2 (2x 3) 3(2x 3) 2 2 2 2 (x 8x) 22( x 8x) 120
二、用因式分解法解下列方程
(1) a2 — 7a+6=0 ;
⑵8x2+6x — 35=0 ;
(3) 18x2 — 21x+5=0 ;
⑸2x2+3x+1=0 ;
⑷ 20 — 9y — 20y2=0；
⑹2y2+y—6=0 ;
(7)6x2— 13x+6=0 ;
(8)3a2 — 7a — 6=0;
(9)6x2— 11x+3=0 ;
(10)4m2+8m+3=0 ;
(11)10x2 — 21x+2=0 ;
(12)8m2 — 22m+15=0 ; 学乐教育数学
理科不好就找乐普
(13)4n2+4n - 15=0 ;
(15)5x2-8x- 13=0 ;
(18)6y2+19y+10=0 ;
(19) 2(a+b) 2+(a+b)(a - b) - 6(a - b) 2=0 ；
-20=0(14)6a2+a - 35=0;
(16)4X2+15X+9=0 ;
(17)15X2+X - 2=0;
(20)7(x - 1) 2+4(x - 1) 学乐教育数学
理科不好就找乐普
答案：十子相乘分解因式:
分解因式:
分解因 2 x 2 x 2 x 2 x 2 x 2 x 2 x
2 x 式： <2 2X2X X
x(x(x XX
X
X
((
3X6)())分解因式: T—
2)1)2
5 XX
X2X
2x2
2x2
3x2
3x2
5x2
6x2 155X
XX
XX /X X2
20
X (2 (x(xx 9 5^
XXX 2
XX (1 x(x X.7/..V
.) T—
3
5 ^12 X 2 14) 2
XXX 3 12
2 2 x 3 x a> a (x a)【x (a 1)] 4
3x 10x 3x x(3x 1)(x 3) x x4 10x2 9 (x 3)( x 3)( x 1)(x 1) (2x 3)2 2 3(2x 23) 2 2(x 1)(2x 1) (x2 8x)2 22( x2
8x) 120 (x2 8x 参考答案：
(I) (a-6)(a-1),
(3)(3x-1) (6x-5),
⑸(x+1) (2x+1),
(7)(2x-3) (3x-2),
(9)(2x-3) (3x-1),
(II) (x-2)(10x-1),
(13) (2n+5) (2n-3),
(15)(x+1)(5x-13),
(17) (3x-1) (5x=2),
(19) (3a-b) (5b-a), 32
2 X2 2 > 2 2
2 -X2 -3 X2 -
5
X 6 X 2 /.V 6xxxx
X
X
X ) X3
X
7
X X
3 X
X G2
1 X K X X > 3 1
x3 4x2 21x x(x 7)( x
6x2 27 (x 3)( x 3)(x2 3)
10)( x 2)( x 6)
⑵(2x+5) (4x-7) (4)-(4y-5)(5y+4)
⑹(y+2) (2y-3)
(8)(a-3)(3a+2)
(10) (2m+1) (2m+3)
(12) (2m-3) (4m-5)
(14) (2a+5) (3a-7)
(16) (x+3) (4x+3)
(18) (2y+5) (3y+2)
(20) (x+1)(7x-17) 13
117
4
1
.)
2
3 )5 T—
3)