Question

factor completely. 2p² + 9p + 7

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times7 = 14\) and add up to \(9\). The numbers are \(2\) and \(7\) since \(2\times7 = 14\) and \(2 + 7=9\).

Step2: Split the middle term

Rewrite the middle term \(9p\) as \(2p+7p\):
\(2p^{2}+2p + 7p+7\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((2p^{2}+2p)+(7p + 7)\)
Factor out the greatest common factor from each group:
\(2p(p + 1)+7(p + 1)\)

Step4: Factor out the common binomial

Factor out \((p + 1)\) from both terms:
\((2p + 7)(p + 1)\)

Answer:

\((2p + 7)(p + 1)\)