Question

Phân tích đa thức thành nhân tử

( x + 1 ) (x + 2) (x+3) (x+4) - 24

Answer 1

\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)

\(=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)

Đặt \(x^2+5x+4=t\)

\(\Rightarrow\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24=t\left(t+2\right)-24\)

\(=t^2+2t+1-25\)

\(=\left(t+1\right)^2-5^2\)

\(=\left(t+1+5\right)\left(t+1-5\right)\)

\(=\left(t+6\right)\left(t-4\right)\)

\(=x\left(x+5\right)\left(x^2+5x+10\right)\)