Determine whether $(x + 4)$ is a factor of $x^{3} + 3 x^{2} - 5 x + 36$ .

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Solution

According to factor theorem, when $f (x)$ is divided by $(x + 4), f (- 4) = 0$
$f (x) = x^{3} + 3 x^{2} - 5 x + 36$
$f (- 4) = (- 4)^{3} + 3 (- 4)^{2} - 5 (- 4) + 36$
$= - 64 + 48 + 20 + 36 = 40$
$∵ f (- 4) \neq 0, (x + 4)$ is not a factor of the given polynomial.

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