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

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Answer 1 · 2018-03-15T18:30:26

See below.

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

$therefore$ let $f(x)=x^2-3x-4$

$f(4) = 4^2-3(4)-4 = 16-12-4$
$=16-16$
$=0$

$therefore (x-4)$ is a factor.

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