Question

Phân tích đa thức sau thành nhân tử:

a) (x² + 3x + 1)(x² + 3x + 2) - 6

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

c) (x² + 3x + 2)(x² + 7x + 12) + 1

Answer 1

a/ \(=\left(x^2+3x+1\right)^2+\left(x^2+3x+1\right)-6\)

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

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

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

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

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

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

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

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

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

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