Answer
$4(x-3)(x+2)$
Work Step by Step
We are given the expression $4x^{2}-4x-24$. First, we can use the distributive property to factor out 4, the greatest common factor of both terms.
$4x^{2}-4x-24=4(x^{2}-x-6)$
Since the last term of $x^{2}-x-6$ is -6, we need to find two factors of -6 that have a sum of -1.
We know that -3 and 2 are factors of -6. Also, $-3\times2=-6$ and $-3+2=-1$.
Therefore, $4(x^{2}-x-6)$ can be factored as $4(x-3)(x+2)$.
