Question

làm giúp e nha mn, thanks mn nhiều lắm ạ

phân tích đa thức thành nhân tử:

a, x^4+x^3+3x^2+2x+2

b, 2x^3+x^2-4x-12

c, x^3-9x^2+14x

d, x^5-xy^4+x^4y-y^5

e, (x+1)(x+3)(x+5)(x+7)-9

Answer 1

b; 2x³+x²-4x-12

= 2x³-4x²+5x²-10x+6x-12

=(2x3-4x2)+(5x2-10x)+(6x-12)

=2x²(x-2)+ 5x(x-2)+6(x-2)

= (x-2)(2x²+5x

Answer 2

con a) mik cứ thấy sai sai nên bn xem lại nhé:

b) 2x³ + x² - 4x - 12

= 2x³ - 4x² + 5x² - 10x + 6x - 12

= (2x³ - 4x²) + (5x² - 10x) + (6x - 12)

= 2x²(x - 2) + 5x(x - 2) + 6(x - 2)

= (2x² + 5x + 6)(x - 2)

= (2x² + 2x + 3x + 6)(x - 2)

= [(2x² + 2x) + (3x + 6)](x - 2)

= [2x(x + 2) + 3(x + 2)](x - 2)

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

= (2x + 3)(x² - 4)

c) x³ - 9x² + 14x

= x³ - 7x² - 2x² + 14x

= (x³ - 7x²) - (2x² - 14x)

= x²(x - 7) - 2x(x - 7)

= (x² - 2x)(x - 7)

= x(x - 2)(x - 7)

d) x⁵ - xy⁴ + x⁴y - y⁵

= (x⁵ + x⁴y) - (xy⁴ + y⁵)

= x⁴(x + y) - y⁴(x + y)

= (x⁴ - y⁴)(x + y)

= (x² + y²)(x² - y²)(x + y)

= (x² + y²)(x - y)(x + y)(x + y)

= (x² + y²)(x - y)(x + y)²

e) (x + 1)(x + 3)(x + 5)(x + 7) - 9

= [(x + 1)(x + 7)][(x + 3)(x + 5)] - 9

= (x² + 7x + x + 7)(x² + 5x + 3x + 15) - 9

= (x² + 8x + 7)(x² + 8x + 15) - 9

Thay x² + 8x + 7 = y, ta có:

y(y + 8) - 9

= y² + 8y - 9

= y² - y + 9y - 9

= (y² - y) + (9y - 9)

= y(y - 1) + 9(y - 1)

= (y + 9)(y - 1)

= (x² + 8x + 7 + 9)(x² + 8x + 7 - 1)

= (x² + 8x + 16)(x² + 8x + 6)

= (x + 4)².(x² + 8x + 6)

NHỚ TIK MK NHÉ

Answer 3

e, (x+1)(x+3)(x+5)(x+7)-9

= [(x+1)(x+7)][(x+3)(x+5)]-9

= (x²+7x+x+7)(x²+5x+3x+15)-9

= (x²+8x+7)(x²+8x+15)-9

đặt x²+8x+7=a

= a(a+8)-9

=a²+8a-9

=x²+9x-x-9

=x(x+9)-1(x+9)

=(x-1)(x+9)

thay a=x²+8x+7 vào ta đc

(x2+8x+7-1)(x2+8x+7+9)

= (x2+8x+6)(x2+8x+16)