Question

Phân tích đa thức thành nhân tử

A = (x² + 3x + 2) (x² + 7x + 12) + 1

Answer 1

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

Answer 2

\(A=\left(x^2+3x+2\right)\left(x^2+7x+12\right)+1\)

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

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

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

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

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

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