How do I use the factor theorem to prove x-4 must be a factor of x^2-3x-4?

Mar 15, 2018

See below.

Explanation:

According to factor theorem, if $\left(x - 4\right)$ is a factor then $f \left(4\right)$ will $= 0$

$\therefore$ let $f \left(x\right) = {x}^{2} - 3 x - 4$

$f \left(4\right) = {4}^{2} - 3 \left(4\right) - 4 = 16 - 12 - 4$
$= 16 - 16$
$= 0$

$\therefore \left(x - 4\right)$ is a factor.