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

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Solution

3 and -3 are the two zeros of the polynomial $(x^{4} + x^{3} - 11 x^{2} - 9 x + 18)$

Therefore, $(x - 3) (x + 3) = x^{2} - 9$ is a factor of given polynomial

Therefore, Dividing the given polynomial by $x^{2} - 9$

Therefore, Quotient $q (x) = x^{2} + x - 2$

Other zeros of given polynomial are -2 and 1

So zeros of given polynomial are 1, -2,3 and -3

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