Question

question
factor the trinomial:
$3x^2 + 16x + 5$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times5 = 15\) and add up to \(16\). The numbers are \(15\) and \(1\) since \(15\times1=15\) and \(15 + 1=16\).

Step2: Split the middle term

Rewrite the middle term \(16x\) as \(15x+x\):
\(3x^{2}+15x + x+5\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((3x^{2}+15x)+(x + 5)\)
Factor out the greatest common factor from each group:
\(3x(x + 5)+1(x + 5)\)

Step4: Factor out the common binomial

Factor out \((x + 5)\) from both terms:
\((3x + 1)(x + 5)\)

Answer:

\((3x + 1)(x + 5)\)