If 3 and ‒3 are two zeros of the polynomial (x^{4} + x^{3} ‒ 11x^{2} ‒ 9x + 18), find all the zeros of the given polynomial.

Let us assume f (x) = x^{4} + x^{3} ‒ 11x^{2} ‒ 9x + 18

As 3 and – 3 are the zeros of the given polynomial therefore each one of (x + 3) and (x - 3) is a factor of f (x)

Consequently, (x – 3) (x + 3) = (x^{2} – 9) is a factor of f (x)

Now, on dividing f (x) by (x^{2} – 9) we get:

f (x) = 0

(x^{2} + x – 2) (x^{2} – 9) = 0

(x – 1) (x + 2) (x – 3) (x + 3) = 0

∴ x = 1 or x = - 2 or x = 3 or x = - 3

Hence, all the zeros of the given polynomial are 1, -2, 3 and -3

14