Question

factor.
$x^2 - 3x - 18$
answer attempt 1 out of 2

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -18 (the constant term) and add up to -3 (the coefficient of the middle term). Let's list the factor pairs of -18:

• 1 and -18: \(1 + (-18)= -17\)
• 2 and -9: \(2 + (-9)= -7\)
• 3 and -6: \(3 + (-6)= -3\) (This is the pair we need)

Step2: Factor the quadratic

Using the numbers 3 and -6, we can rewrite the middle term of the quadratic \(x^{2}-3x - 18\) as \(x^{2}+3x - 6x - 18\). Then, we factor by grouping:
\[

$$\begin{align*} x^{2}+3x - 6x - 18&=x(x + 3)-6(x + 3)\\ &=(x - 6)(x + 3) \end{align*}$$

\]

Answer:

\((x - 6)(x + 3)\)