Question

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

Answer 1

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