Is x+4 a factor of 2x^3+3x^2-29x-60?

Sep 19, 2016

$\left(x + 4\right)$ is not a factor of $f \left(x\right) = 2 {x}^{3} + 3 {x}^{2} - 29 x - 60$

Explanation:

According to factor theorem if $\left(x - a\right)$ is a factor of polynomial $f \left(x\right)$, then $f \left(a\right) = 0$.

Here we have to test for $\left(x + 4\right)$ i.e. $\left(x - \left(- 4\right)\right)$. Therefore, if $f \left(- 4\right) = 0$ then $\left(x + 4\right)$ is a factor of $f \left(x\right) = 2 {x}^{3} + 3 {x}^{2} - 29 x - 60$.

$f \left(- 4\right) = 2 {\left(- 4\right)}^{3} + 3 {\left(- 4\right)}^{2} - 29 \left(- 4\right) - 60$

= 2×(-64)+3×16-29×(-4)-60

= $- 128 + 48 + 116 - 60$

= $164 - 188 = - 24$

Hence $\left(x + 4\right)$ is not a factor of $f \left(x\right) = 2 {x}^{3} + 3 {x}^{2} - 29 x - 60$.