Question

Phân tích các đa thức sau thành nhân tử:

A) \(2x^2+7x+5\)

B) \(x^2-4x-5\)

C) \(x^4+x^3+x+1\)

D) \(x^4+4x^2-5\)

Mình đang cần lời giải (chi tiết). Cảm ơn

Answer 1

A/ \(2x^2+7x+5=2\left(x^2+2x+1\right)+3x+3=2\left(x+1\right)^2+3\left(x+1\right)\)

\(=\left(x+1\right)\left(2x+5\right)\)

B/ \(x^2-4x-5=\left(x^2-4x+4\right)-9=\left(x-2\right)^2-3^2=\left(x-5\right)\left(x+1\right)\)

C/ \(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)

D/\(x^4+4x^2-5=\left(x^4+4x^2+4\right)-9=\left(x^2+2\right)^2-3^2=\left(x^2-1\right)\left(x^2+5\right)=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)

Answer 2

a) = 2x^2 + 2x +5x + 5 = 2x(x+1) + 5(x+1) = (2x+5)(x+1)

b) = x^2 + x - 5x - 5 = x(x-1) - 5(x-1) = (x-5)(x-1)

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

d) = x^4 - x^2 + 5x^2 -5 = x^2 (x^2-1) + 5(x^2-1) = (x^2+5)(x-1)(x+1)