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Division of a Polynomial by a Monomial

Determine whe...

Question

Determine whether $(x + 1)$ is a factor of the polynomial:
$2 x^{4} + 9 x^{3} + 2 x^{2} + 10 x + 15$

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Solution

According to factor theorem, when $f (x)$ is divided by $(x + 1)$ , $f (- 1) = 0$
$f (x) = 2 x^{4} + 9 x^{3} + 2 x^{2} + 10 x + 15$
$f (- 1) = 2 (- 1)^{4} + 9 (- 1)^{3} + 2 (- 1)^{2} + 10 (- 1) + 15$
$= 2 - 9 + 2 - 10 + 15 = 0$
$∵ f (- 1) = 0, (x + 1)$ is a factor of the given polynomial.

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