Question

online savvas 7-5 day 1
factor the expression.
$x^2 - 14x - 32$
$x^2 - 14x - 32 = \square$
(type your answer in factored form.)

Explanation:

Step1: Find pair of factors of -32

We need two numbers that multiply to $-32$ and add to $-14$. These numbers are $-16$ and $2$, since $(-16) \times 2 = -32$ and $(-16) + 2 = -14$.

Step2: Rewrite middle term using factors

$$x^2 - 16x + 2x - 32$$

Step3: Group and factor by grouping

Group the first two and last two terms:
$$(x^2 - 16x) + (2x - 32)$$
Factor out the GCF from each group:
$$x(x - 16) + 2(x - 16)$$

Step4: Factor out common binomial

Factor out $(x - 16)$ from both terms:
$$(x - 16)(x + 2)$$

Answer:

$(x - 16)(x + 2)$