Question

factor.
$x^2 - x - 12$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-12\) (the constant term) and add up to \(-1\) (the coefficient of \(x\)). Let's list the factor pairs of \(-12\): \((-4, 3)\) because \(-4\times3 = -12\) and \(-4 + 3=-1\).

Step2: Factor the quadratic

Using the numbers found, we can factor \(x^{2}-x - 12\) as \((x - 4)(x + 3)\). We check by expanding: \((x - 4)(x + 3)=x^{2}+3x-4x - 12=x^{2}-x - 12\), which matches the original quadratic.

Answer:

\((x - 4)(x + 3)\)