Question

Bài 2: Phân tích đa thức thành nhân tử:  tách một hạng tử thành nhiều hạng)

a, 3x² - 5x - 2

b, 2x² + x - 6

c, 7x² + 50x + 7

d, 12x² + 7x - 12

e, 15x² + 7x - 2

f, a² - 5a - 14

g, 2m² + 10m + 8

h, 4p² - 36p + 56

i, 2x² + 5x + 2

Answer 1

`a)3x^2-5x+2`

`=(3x^3-3x)+(-2x+2)`

`=3x(x-1)-2(x-1)`

`=(3x-2)(x-1)`

`b)2x^2+x-6`

`=(2x^2-3x)+(4x-6)`

`=x(2x-3)+2(2x-3)`

`=(2x-3)(x+2)`

`c)7x^2+50x+7`

`=(7x^2+49x)+(x+7)`

`=7x(x+7)+(x+7)`

`=(x+7)(7x+1)`

`d)12x^2+7x-12`

`=(12x^2-9x^2)+(16x-12)`

`=3x(4x-3)+4(4x-3)`

`=(4x-3)(3x-4)`

`e)15x^2+7x-2`

`=(15x^2-3x)+(10x-2)`

`=3x(5x-1)+2(5x-1)`

`=(5x-1)(3x+2)`

Answer 2

a)
\(3x^2-5x-2\\ =3x^2+x-6x-2\\ =\left(3x^2+x\right)-\left(6x+2\right)\\ =x.\left(3x+1\right)-2.\left(3x+1\right)\\ =\left(3x+1\right).\left(x-2\right)\)

b) 
\(2x^2+x-6\\ =2x^2+4x-3x-6\\ =\left(2x^2+4x\right)-\left(3x+6\right)\\ =2x.\left(x+2\right)-3.\left(x+2\right)\\ =\left(x+2\right).\left(2x-3\right)\)

c) 
\(7x^2+50x+7\\ =7x^2+49x+x+7\\ =\left(7x^2+49x\right)+\left(x+7\right)\\ =7x.\left(x+7\right)+\left(x+7\right)\\ =\left(x+7\right).\left(7x+1\right)\)
 

Answer 3

d)
\(12x^2+7x-12\\ =12x^2-9x+16x-12\\ =\left(12x^2-9x\right)+\left(16x-12\right)\\ =3x.\left(4x-3\right)+4.\left(4x-3\right)\\ =\left(4x-3\right).\left(3x+4\right)\)

e)
\(15x^2+7x-2\\ =15x^2+10x-3x-2\\ =\left(15x^2+10x\right)-\left(3x+2\right)\\ =5x.\left(3x+2\right)-\left(3x+2\right)\\ =\left(3x+2\right).\left(5x-1\right)\)

f)
\(a^2-5a-14\\ =a^2+2a-7a-14\\ =\left(a^2+2a\right)-\left(7a+14\right)\\ =a.\left(a+2\right)-7.\left(a+2\right)\\ =\left(a+2\right).\left(a-7\right)\)

Answer 4

g)
 \(2m^2+10m+8\\ =2m^2+2m+8m+8\\ =\left(2m^2+2m\right)+\left(8m+8\right)\\ =2m.\left(m+1\right)+8.\left(m+1\right)\\ =\left(m+1\right).\left(2m+8\right)\\ =2.\left(m+1\right).\left(m+4\right)\)

h)
\(4p^2-36p+56\\ =4p^2-8p-28p+56\\ =\left(4p^2-8p\right)-\left(28p-56\right)\\ =4p.\left(p-2\right)-28.\left(p-2\right)\\ =\left(p-2\right).\left(4p-28\right)\\ =4.\left(p-2\right).\left(p-7\right)\)

Answer 5

i) 
\(2x^2+5x+2\\ =2x^2+4x+x+2\\ =\left(2x^2+4x\right)+\left(x+2\right)\\ =2x.\left(x+2\right)+\left(x+2\right)\\ =\left(x+2\right).\left(2x+1\right)\)