Question

x³ + 13x² + 32x + 20

Answer 1

Let `f(x) = x^3 + 13x^2 + 32x + 20` be the given polynomial.

Now, putting   x= -1,we get

`⇒ f(-1) = (-1)^3 + 13(-1)^2 + 32(-1) + 20`

                    ` = -1 + 13 - 32 + 20 = -33 + 33`

                    ` =0`

Therefore, (x +1)is a factor of polynomial f(x).

Now,

`f(x) = x^2 (x+1)+12x (x+1)+20(x+1)`

       ` = (x+1){x^2 + 12x + 20}`

       ` = (x+1){x^2 + 10x + 2x + 20}`

       `  = (x+1)(x+2)(x + 10)`

Hence   
(x +1),(x+2)  and (x+10) are the factors of polynomial f(x).