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

Explanation

Let `p(x) = x^3 + 13x^2 + 32x + 20`
`p(-1) = -1 + 13 - 32 + 20 = -33 + 33 = 0`
Therefore `(x + 1)` is a factor of `p(x)`.
On dividing `p(x)` by `(x + 1)` we get
`p(x) (x + 1) = x^2 + 12x + 20`
Thus,
`x^3 + 13x^2 + 32x + 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 +2) (x + 10)`