Question

phân tích đa thức sau thành nhân tử

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

nhanh mk tick nhé

Answer 1

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

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

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-3\)(1)

Đặt \(x^2+5x=t\)

\(\Rightarrow\left(1\right)=t\left(t+2\right)-3=t^2+2t-3\)

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

\(=\left(t-1\right)\left(t+3\right)\)(2)

Mà \(x^2+5x=t\)nên \(\left(2\right)=\left(x^2+5x-1\right)\left(x^2+5x+3\right)\)

hay \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-3\)\(=\left(x^2+5x-1\right)\left(x^2+5x+3\right)\)