Question

question
factor.
$x^2 - 7x - 18$
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 $-7$ (the coefficient of the $x$ term). Let's list the factor pairs of $18$: $1$ and $18$, $2$ and $9$, $3$ and $6$. Since the product is negative, one number is positive and the other is negative. We need a pair where the negative number has a larger absolute value (because their sum is $-7$). The pair $2$ and $-9$ works because $2\times(-9) = -18$ and $2 + (-9) = -7$.

Step2: Factor the quadratic

Using the numbers we found, we can factor the quadratic $x^2 - 7x - 18$ as $(x + 2)(x - 9)$. Let's check: $(x + 2)(x - 9) = x^2 - 9x + 2x - 18 = x^2 - 7x - 18$, which matches the original expression.

Answer:

$(x + 2)(x - 9)$