Question

Phân tích đa thức sau thành nhân tử

a,\(\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)

b,\(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)

Answer 1

a) Đặt \(t=x^2+8x+7\)

Ta có : \(t.\left(t+8\right)+15\)

\(=t^2+8t+15\)

\(=t^2+5t+3t+15\)

\(=\left(t^2+5t\right)+\left(3t+15\right)\)

\(=t\left(t+5\right)+3\left(t+5\right)\)

\(=\left(t+3\right)\left(t+5\right)\)

Mà : \(t=x^2+8x+7\)

Suy ra : \(\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)

b) Đặt : \(a=x^2+x+1\)

Ta có : \(a\left(a+1\right)-12\)

\(=a^2+a-12\)

\(=a^2+2a-6a-12\)

\(=\left(a^2+2a\right)-\left(6a+12\right)\)

\(=a\left(a+2\right)-6\left(a+2\right)\)

\(=\left(a-6\right)\left(a+2\right)\)

Mà : \(a=x^2+x+1\)

Nên : \(\left(x^2+x-5\right)\left(x^2+x+3\right)\)