Question

factor.
$x^2 + 3x - 18$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-18\) and add up to \(3\). Let's list the factor pairs of \(-18\): \((-1, 18)\), \((1, -18)\), \((-2, 9)\), \((2, -9)\), \((-3, 6)\), \((3, -6)\). Among these, \(-3\) and \(6\) multiply to \(-18\) (\(-3\times6 = -18\)) and add up to \(3\) (\(-3 + 6 = 3\)).

Step2: Rewrite the middle term

Using the two numbers we found, we rewrite the middle term of the quadratic expression. So, \(x^{2}+3x - 18\) becomes \(x^{2}-3x + 6x - 18\).

Step3: Group and factor

Group the first two terms and the last two terms: \((x^{2}-3x)+(6x - 18)\). Factor out the greatest common factor from each group. From the first group, we can factor out \(x\) to get \(x(x - 3)\). From the second group, we can factor out \(6\) to get \(6(x - 3)\). Now our expression is \(x(x - 3)+6(x - 3)\).

Step4: Factor out the common binomial

We can see that both terms have a common binomial factor of \((x - 3)\). Factoring that out, we get \((x - 3)(x + 6)\).

Answer:

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