How do you use the factor theorem to determine whether x+2 is a factor of $x^{4} - 3 x - 5$ $x^4 - 3x - 5$ ?

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Answer 1 · 2015-12-01T11:36:40

According to the Factor Theorem
$f (- 2) = 0$ $f(-2)=0$ if and only if $(x + 2)$ $(x+2)$ is a factor of $f (x)$ $f(x)$

Given $f (x) = x^{4} - 3 x - 5$ $f(x)=x^4-3x-5$

$f (- 2) = {(- 2)}^{4} - 3 \cdot (- 2) - 5 = 16 + 6 - 5 = 17 \neq 0$ $f(-2) = (-2)^4-3*(-2)-5 =16+6-5 = 17 !=0$

and therefore $(x + 2)$ $(x+2)$ is not a factor of $f (x) = x^{4} - 3 x - 5$ $f(x)=x^4-3x-5$

How do you use the factor theorem to determine whether x+2 is a factor of x^4 - 3x - 5x4−3x−5x^4 - 3x - 5?