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Factor of a Polynomial

Which is a fa...

Question

Which is a factor of $x^{3} + 9 x^{2} - 6 x - 4$ ?

x + 1

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x - 1

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x + 4

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x - 4

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none of the above

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Solution

The correct option is B $x - 1$
The factors of $x^{3} + 9 x^{2} - 6 x - 4$
$= x^{3} - x^{2} + 10 x^{2} - 10 x + 4 x - 4$
$= (x - 1) (x^{2} + 10 x + 4)$
Therefore $x - 1$ is one of the factor.
Therefore the correct answer is $B$ .

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Prove that none of the polynomials listed below has first degree factors:

(i) x² + x + 1

(ii) x⁴ + 1

(iii) x² − x + 1

(iv) x⁴ + x² + 1

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