Question

factor.
$u^{2}+9u + 14$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to 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 \(u^{2}+9u + 14\) as \(u^{2}+2u+7u + 14\).

Step3: Group the terms

Group the terms: \((u^{2}+2u)+(7u + 14)\).

Step4: Factor out the GCF from each group

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

Step5: Factor out the common binomial factor

Factor out \((u + 2)\) to get \((u + 2)(u+7)\).

Answer:

\((u + 2)(u + 7)\)