We know that if x = a is a zero of a polynomial then x - a is a factor of f(x).
Since -2 is zero of f(x)
Therefore (x + 2) is a factor of f(x)
Now on divide f(x) = x3 + 13x2 + 32x + 20 by (x + 2) to find other zeros.
By applying division algorithm, we have:
x 3 + 13x2 + 32x + 20 = (x+2)(x2+11x+10)
We do factorisation here by splitting the middle term,
⇒ x3 + 13x2 + 32x + 20 = (x+2)(x2+11x+10)
⇒ x3 + 13x2 + 32x + 20 = (x+2)(x2+10x+x+10)
⇒ x3 + 13x2 + 32x + 20 = (x+2) {x(x+10)+1(x+10)}
⇒ x3 + 13x2 + 32x + 20 = (x+2) (x+10)(x+1)
Hence, the zeros of the given polynomial are:
-2, -10, -1