Question

(x^2+3x+1)(x^2+3x+2)-6

Answer 1

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

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

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

Answer 2

\(=x^4+3x^3+2x^2+3x^3+9x^2+6x+x^2+3x+2-6=x^4+6x^3+12x^2+9x-4\)

Answer 3

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