Question

question
factor the trinomial:
$2x^2 + 11x + 5$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times5 = 10\) and add up to \(11\). The numbers are \(10\) and \(1\).

Step2: Split the middle term

Rewrite the middle term \(11x\) as \(10x + x\):
\(2x^{2}+10x + x + 5\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((2x^{2}+10x)+(x + 5)\)
Factor out the common factors from each group:
\(2x(x + 5)+1(x + 5)\)

Step4: Factor out the common binomial

Factor out \((x + 5)\):
\((2x + 1)(x + 5)\)

Answer:

\((2x + 1)(x + 5)\)