How do you use the factor theorem to determine whether x-5 is a factor of f(x) = 2x^3 +5x^2 -14x -72?

Dec 5, 2015

$x - 5$ is not a factor of $f \left(x\right)$

Explanation:

To see if $\left(x - 5\right)$ is a factor of $f \left(x\right)$ we have to check if $f \left(5\right) = 0$

$f \left(5\right) = 2 \cdot {5}^{3} + 5 \cdot {5}^{2} - 14 \cdot 5 - 72$

$f \left(5\right) = 250 + 125 - 70 - 72$

$f \left(5\right) = 375 - 142$

$f \left(5\right) = 233$

$f \left(5\right) \ne 0$ so $\left(x - 5\right)$ is not a factor of $f \left(x\right)$