Determine whether $(x + 1)$ is a factor of the polynomial:
$6 x^{4} + 7 x^{3} - 5 x - 4$

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Solution

According to factor theorem, when $f (x)$ is divided by $(x + 1)$ , $f (- 1) = 0$
$f (x) = 6 x^{4} + 7 x^{3} - 5 x - 4$
$f (- 1) = 6 (- 1)^{4} + 7 (- 1)^{3} - 5 (- 1) - 4$
$= 6 - 7 + 5 - 4 = 0$
$∵ f (- 1) = 0$ , we can say that $(x + 1)$ is a factor of the given polynomial

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