Question

求20道整式乘法和20道因式分解

要求：全部是计算题，不能有选择、填空、证明题
例：（x+1）（x+2）=
x²+2x+1=
题要难一点，要有答案

Answer 1

20道分解因式，40道整式乘法，排成 5组

在同一组里面，就有相互变形的结果

• 分解因式，这里还是用分组分解法更好

怎样把一次项一分为二，就由常数项的正负来决定了

一次项不变，只要常数项变成相反数，就要改变一分为二的方式

• 如果常数项是正数，一次项就是拆开两个绝对值比原来小的两项的和；

• 如果常数项是负数，一次项系数就是分开两项的相差数；

动动脑筋，找找规律，感受一下其中的奥秘吧

x" + 5x + 6

x" + 5x - 6

x" - 5x + 6

x" - 5x - 6

( x + 1 )( x + 6 )

( x + 1 )( x - 6 )

( x - 1 )( x + 6 )

( x - 1 )( x - 6 )

( x + 2 )( x + 3 )

( x + 2 )( x - 3 )

( x - 2 )( x + 3 )

( x - 2 )( x - 3 )

x" + 10x + 24

x" + 10x - 24

x" - 10x + 24

x" - 10x - 24

( x + 2 )( x + 12 )

( x + 2 )( x - 12 )

( x - 2 )( x + 12 )

( x - 2 )( x - 12 )

( x + 4 )( x + 6 )

( x + 4 )( x - 6 )

( x - 4 )( x + 6 )

( x - 4 )( x - 6 )

x" + 15x + 54

x" + 15x - 54

x" - 15x + 54

x" - 15x - 54

( x + 3 )( x + 18 )

( x + 3 )( x - 18 )

( x - 3 )( x + 18 )

( x - 3 )( x - 18 )

( x + 6 )( x + 9 )

( x + 6 )( x - 9 )

( x - 6 )( x + 9 )

( x - 6 )( x - 9 )

x" + 20x + 96

x" + 20x - 96

x" - 20x + 96

x" - 20x - 96

( x + 4 )( x + 24 )

( x + 4 )( x - 24 )

( x - 4 )( x + 24 )

( x - 4 )( x - 24 )

( x + 8 )( x + 12 )

( x + 8 )( x - 12 )

( x - 8 )( x + 12 )

( x - 8 )( x - 12 )

x" + 25x + 150

x" + 25x - 150

x" - 25x + 150

x" - 25x - 150

( x + 5 )( x + 30 )

( x + 5 )( x - 30 )

( x - 5 )( x + 30 )

( x - 5 )( x - 30 )

( x + 10 )( x + 15 )

( x + 10 )( x - 15 )

( x - 10 )( x + 15 )

( x - 10 )( x - 15 )

Answer 2

20道整式乘法
(4 x-7) (4 x+1) = 16 x^2-24 x-7
(x-6) (6 x+4) = 6 x^2-32 x-24
(2 x+6) (5 x-7) = 10 x^2+16 x-42
(5 x+3) (9 x-1) = 45 x^2+22 x-3
(6 x-9) (9 x+1) = 54 x^2-75 x-9
(7 x+8) (9 x-2) = 63 x^2+58 x-16
(4 x-8) (5 x+5) = 20 x^2-20 x-40
(2 x-3) (8 x+8) = 16 x^2-8 x-24
(x-3) (7 x+5) = 7 x^2-16 x-15
(6 x-3) (6 x+7) = 36 x^2+24 x-21
(3 x-7) (3 x+8) = 9 x^2+3 x-56
(x+6) (7 x-1) = 7 x^2+41 x-6
(4 x+7) (5 x-4) = 20 x^2+19 x-28
(x+2) (6 x-8) = 6 x^2+4 x-16
(3 x+1) (8 x-2) = 24 x^2+2 x-2
(x-3) (2 x+9) = 2 x^2+3 x-27
(4 x+3) (9 x-5) = 36 x^2+7 x-15
(x-6) (9 x+5) = 9 x^2-49 x-30
(2 x-1) (9 x+1) = 18 x^2-7 x-1
(5 x-1) (8 x+8) = 40 x^2+32 x-8

20道因式分解
21 x^2+50 x-16=(3 x+8) (7 x-2)
14 x^2-36 x-18=2 (x-3) (7 x+3)
42 x^2-2 x-20=(6 x+4) (7 x-5)
8 x^2-8 x-48=8 (x-3) (x+2)
9 x^2+3 x-30=3 (x+2) (3 x-5)
9 x^2+60 x-21=(x+7) (9 x-3)
8 x^2+18 x-5=(2 x+5) (4 x-1)
12 x^2-38 x-40=2 (x-4) (6 x+5)
14 x^2+19 x-40=(2 x+5) (7 x-8)
49 x^2-28 x-12=(7 x-6) (7 x+2)
6 x^2+18 x-24=6 (x-1) (x+4)
15 x^2-22 x-48=(3 x-8) (5 x+6)
42 x^2-6 x-48=6 (x+1) (7 x-8)
40 x^2-17 x-12=(5 x-4) (8 x+3)
2 x^2-12 x-54=2 (x-9) (x+3)
16 x^2+22 x-3=(2 x+3) (8 x-1)
81 x^2+27 x-18=(9 x-3) (9 x+6)
30 x^2+16 x-32=(5 x-4) (6 x+8)
27 x^2-9 x-18=9 (x-1) (3 x+2)
20 x^2-22 x-16=(4 x+2) (5 x-8)

20道整式除法
(15 x^2+18 x-81)/(3 x+9) = 5 x-9
(9 x^2-22 x-15)/(9 x+5) = x-3
(8 x^2-10 x-7)/(2 x+1) = 4 x-7
(25 x^2+35 x-18)/(5 x+9) = 5 x-2
(45 x^2-2 x-8)/(5 x+2) = 9 x-4
(72 x^2+20 x-28)/(9 x+7) = 8 x-4
(32 x^2+4 x-6)/(4 x+2) = 8 x-3
(40 x^2+43 x-6)/(5 x+6) = 8 x-1
(12 x^2+15 x-63)/(3 x+9) = 4 x-7
(36 x^2-33 x-15)/(9 x+3) = 4 x-5
(72 x^2+21 x-15)/(8 x+5) = 9 x-3
(45 x^2+46 x-63)/(5 x+9) = 9 x-7
(54 x^2+54 x-24)/(6 x+8) = 9 x-3
(5 x^2+x-18)/(x+2) = 5 x-9
(27 x^2+30 x-8)/(3 x+4) = 9 x-2
(15 x^2-x-2)/(3 x+1) = 5 x-2
(7 x^2-52 x-32)/(7 x+4) = x-8
(54 x^2+3 x-35)/(6 x+5) = 9 x-7
(6 x^2-7 x-20)/(3 x+4) = 2 x-5
(3 x^2-x-24)/(3 x+8) = x-3