Question

Phân tích đa thức thành nhân tử : A= ( x^2 - y^2 + 2x) + 1 B=x^4 + 64y^4 C= ( x^2 + x)^2 + 2.(x^2 + x)-3 D= (x^2 - 4x)^2 +7(x^2- 4x)+12

Answer 1

A = (x^2 - y^2 + 2x) + 1 = (x^2 + 2x + 1)-y^2 = (x+1)^2 - y^2 =

(x+1-y)(x+1+y)

B = x^4 - 64y^4 = (x^2)^2 - (8y^2)^2 = (x^2 - 8y^2 ) (x^2 + 8y^2 )

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

= (x^2 + x)^2 + 2(x^2 + x) + 1 - 2^2

= (x^2 + x + 1) - 2^2 = (x^2 + x + 1 - 2)(x^2 + x + 1 + 2 )

= (x^2 + x - 1)(x^2 + x + 3)

D = (x^2 - 4x)^2 + 7(x^2 - 4x) + 12

= (x^2 - 4x)^2 + 2(x^2 - 4x). 7/2 + 49/4 - 1/4

= (x^2 - 4x + 7/2)^2 - 1/4

= (x^2 - 4x + 7/2 - 1/4)(x^2 - 4x + 7/2 + 1/4)

= (x^2 - 4x + 13/4)(x^2 - 4x +15/4)

Answer 2

D = (x^2 - 4x)^2 + 7(x^2 - 4x) + 12

= (x^2 - 4x)^2 + 2(x^2 - 4x).7/2 + 49/4 - 1/4

= (x^2 - 4x + 7/2)^2 - 1/4

= (x^2 - 4x + 7/2 - 1/2)(x^2 - 4x + 7/2 + 1/2)

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