Question

(x+5) (x-4) (x+3) (x-2) (x+1) x - (x^2 + x^3)

Answer 1

$\left(x+5\right)\left(x-4\right)\left(x+3\right)\left(x-2\right)\left(x+1\right)x-\left(x^2+x^3\right)$
$=x\left(x-4\right)\left(x+5\right)\left(x+1\right)\left(x+3\right)\left(x-2\right)-x^2\left(x+1\right)$
$=x\left(x+1\right)\left(\left(x-4\right)\left(x+5\right)\left(x+3\right)\left(x-2\right)-x\right)$
$=x\left(x+1\right)\left(x^4+2x^3-25x^2-27x+120\right)$