Question

Phân tích đa thức thành nhân tử:

(x² + x).(x² + x + 4) - 60

Answer 1

Đặt \(x^2+x+2=t\) .Khi đó:

\(\left(x^2+x\right)\left(x^2+x+4\right)-60\)

\(=\left(t-2\right)\left(t+2\right)-60=t^2-6-60=t^2-64=\left(t-8\right)\left(t+8\right)\)

\(=\left(x^2+x+2-8\right)\left(x^2+x+2+8\right)=\left(x^2+x-6\right)\left(x^2+x+10\right)\)

\(=\left(x-2\right)\left(x+3\right)\left(x^2+x+10\right)\)

 

Answer 2

Đặt \(t=x^2+x+2\) 

Suy ra \(\left(x^2+x\right)\left(x^2+x+4\right)-60=\left(t-2\right)\left(t+2\right)-60=t^2-8^2=\left(t-8\right)\left(t+8\right)\)

\(=\left(x^2+x-6\right)\left(x^2+x+10\right)=\left(x+3\right)\left(x-2\right)\left(x^2+x+10\right)\)