Is $(x + 5)$ a factor of $x^{3} + 2 x^{2} - 14 x + 9 ?$

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Solution

Is $(x + 5)$ a factor of $x^{3} + 2 x^{2} - 14 x + 9$
$(x + a)$ is a factor of $p (x)$ if $p (- a) = 0$
Put $a = 5$
$p (x) = x^{3} + 2 x^{2} - 14 x + 9$
$p (- 5) = (- 5)^{3} + 2 (- 5)^{2} - 14 (- 5) + 9$
$= - 125 + 50 + 70 + 9$
$= - 125 + 129$
$\Rightarrow 4$
$P (- 5) = 4 \neq 0$
$∴ (x + 5)$ is not a factor of $x^{3} + 2 x^{2} - 14 x + 9$ .

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