Question

question
factor completely.
$2x^2 + 9x + 7$

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: Rewrite the middle term

Rewrite \(9x\) as \(2x + 7x\) in the expression \(2x^{2}+9x + 7\), so we get \(2x^{2}+2x+7x + 7\).

Step3: Group the terms

Group the first two terms and the last two terms: \((2x^{2}+2x)+(7x + 7)\).

Step4: Factor out the GCF from each group

Factor out \(2x\) from the first group and \(7\) from the second group: \(2x(x + 1)+7(x + 1)\).

Step5: Factor out the common binomial factor

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

Answer:

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