Question

question
factor.
$x^2 - 7x - 18$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-18\) and add up to \(-7\). Let's list the factor pairs of \(-18\): \((-9, 2)\) because \(-9\times2 = -18\) and \(-9 + 2=-7\).

Step2: Factor the quadratic

Using the numbers we found, we can factor \(x^{2}-7x - 18\) as \((x - 9)(x + 2)\). Because when we expand \((x - 9)(x + 2)\) using the distributive property (FOIL method), we get \(x^{2}+2x-9x - 18=x^{2}-7x - 18\), which matches the original quadratic.

Answer:

\((x - 9)(x + 2)\)