Question

Phân tích đa thức sau thành nhân tử:

(x+1)(x+2)(x+3)(x+4)-120

Answer 1

\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-120\)

\(=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)-120\)

\(=\left(x^2+4x+x+4\right)\left(x^2+2x+3x+6\right)-120\)

\(=\left(x^2+5x+5-1\right)\left(x^2+5x+5+1\right)-120\)

\(=\left(x^2+5x+5\right)^2-121\)

\(=\left(x^2+5x+5+11\right)\left(x^2+5x+5-11\right)\)

\(=\left(x^2+5x+16\right)\left(x^2+5x-6\right)\)

\(=\left(x-3\right)\left(x-2\right)\left(x^2+5x+16\right)\)