Question

question
factor completely.
$2x^2 + 15x + 7$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times7 = 14\) and add up to \(15\). The numbers are \(1\) and \(14\) since \(1\times14 = 14\) and \(1 + 14=15\).

Step2: Split the middle term

Rewrite the middle term \(15x\) as \(x+14x\):
\(2x^{2}+x + 14x+7\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((2x^{2}+x)+(14x + 7)\)
Factor out the greatest common factor from each group:
\(x(2x + 1)+7(2x + 1)\)

Step4: Factor out the common binomial

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

Answer:

\((2x + 1)(x + 7)\)