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Factor Theorem

Find all the ...

Question

Find all the zeros of the polynomial x⁴ + x³ − 34x² − 4x + 120, if two of its zeros are 2 and −2.

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Solution

We know that if is a zero of a polynomial, then is a factor of .

Since, and are zeros of .

Therefore

is a factor of .Now, we divide by to find the other zeros of .

By using division algorithm we have

Hence, the zeros of the given polynomial are .

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