Question

factor completely.
$p^2 + 2p - 8$

Explanation:

Step1: Analyze the quadratic expression

We have the quadratic expression \( p^2 + 2p - 8 \). We need to find two numbers that multiply to \( -8 \) (the constant term) and add up to \( 2 \) (the coefficient of the middle term).

Step2: Find the two numbers

The numbers \( 4 \) and \( -2 \) satisfy the conditions because \( 4\times(-2)=-8 \) and \( 4 + (-2)=2 \).

Step3: Factor the expression

We can rewrite the middle term using these two numbers:
\( p^2 + 4p - 2p - 8 \)
Now, group the terms:
\( (p^2 + 4p) + (-2p - 8) \)
Factor out the greatest common factor from each group:
\( p(p + 4) - 2(p + 4) \)
Now, factor out the common binomial factor \( (p + 4) \):
\( (p + 4)(p - 2) \)

Answer:

\( (p + 4)(p - 2) \)