Factorize `x^3+13 x^2+32 x+20 ,` if it is given that `x+2` is its factor.

Explanation

`x^3+13x^2+32x+20`
`= x^3 + x^2+ 12x^2 + 12x + 20x + 20`
`=x^2(x+1) + 12x(x+1) +20(x+1)`
`=(x^2 + 12x + 20)(x+1)`
`=(x^2 + 10x + 2x + 20)(x + 1)`
`={x(x + 10) + 2(x + 10)}(x + 1)`
`=(x+1)(x+2)(x+10)`