Obtain all zeros of f(x) = x³ + 13x² + 32x + 20 if one of its zeros is –2.

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:

x³ + 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