Question

Phân tích đa thức thành nhân tử

\(\left(x^2+x\right)^2-5\left(x^2+x\right)+6\)

Answer 1

\(\left(x^2+x\right)^2-5\left(x^2+x\right)+6\\ =\left[\left(x^2+x\right)^2-2\left(x^2+x\right)\right]+\left[-3\left(x^2+x\right)+6\right]\\ =\left(x^2+x\right)\left[\left(x^2+x\right)-2\right]-3\left[\left(x^2+x\right)-2\right]\\ =\left(x^2+x-2\right)\left(x^2+x\right)-\left(x^2+x-2\right)\cdot\left(-3\right)\\ =\left(x^2+x-2\right)\left(x^2+x-3\right)\)

Answer 2

Đặt \(x^2+x=t\) ,ta có:

\(t^2-5t+6\)

\(=\left(t-2\right)\left(t-3\right)\)

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