Question

factor completely.\\(2u^2 + 9u + 10\\)

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times10 = 20\) and add up to \(9\). The numbers are \(4\) and \(5\) since \(4\times5 = 20\) and \(4 + 5=9\).

Step2: Rewrite the middle term

Rewrite \(9u\) as \(4u+5u\) in the quadratic expression: \(2u^{2}+4u + 5u+10\).

Step3: Group the terms

Group the first two and the last two terms: \((2u^{2}+4u)+(5u + 10)\).

Step4: Factor out the GCF from each group

Factor out \(2u\) from the first group and \(5\) from the second group: \(2u(u + 2)+5(u + 2)\).

Step5: Factor out the common binomial factor

Factor out \((u + 2)\) from both terms: \((2u + 5)(u + 2)\).

Answer:

\((2u + 5)(u + 2)\)