Question

e trinomial:
$3x^2 + 14x + 8$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times8 = 24\) and add up to \(14\). The numbers are \(12\) and \(2\) since \(12\times2 = 24\) and \(12 + 2=14\).

Step2: Split the middle term

Rewrite the middle term \(14x\) as \(12x+2x\) in the trinomial:
\(3x^{2}+12x + 2x+8\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((3x^{2}+12x)+(2x + 8)\)
Factor out the greatest common factor from each group:
\(3x(x + 4)+2(x + 4)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x + 4)\):
\((3x + 2)(x + 4)\)

Answer:

\((3x + 2)(x + 4)\)