# How do you use the factor theorem to determine whether x-5 is a factor of 3x^3 - 12x^2 - 11x - 20?

Nov 15, 2015

Since $f \left(5\right) = 0$
$\textcolor{w h i t e}{\text{XXX}}$(for $f \left(x\right) = 3 {x}^{3} - 12 {x}^{2} - 11 x - 20$)
$\left(x - 5\right)$ is a factor of (f(x)

#### Explanation:

The Factor Theorem says that $\left(x - a\right)$ is a factor of $f \left(x\right)$ if and only if $f \left(a\right) = 0$

You could use a calculator, synthetic substitution (below), paper and pencil, or many other ways to evaluate $3 {x}^{3} - 12 {x}^{2} - 11 x - 20$ at $x = 5$

Evaluation using synthetic substitution:
{: (,,3,-12,-11,-20), (,,,color(white)("X")15,color(white)("X")15,color(white)("X")20), (,,"----","-----","-----","-----"), (xx(5),"|",3,color(white)("X")3,color(white)("X")4,color(white)("X")color(red)(0)) :}