Question

question
factor the trinomial:
$3x^2 + 13x + 4$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times4 = 12\) and add up to \(13\). The numbers are \(12\) and \(1\) since \(12\times1 = 12\) and \(12 + 1=13\).

Step2: Split the middle term

Rewrite the middle term \(13x\) as \(12x+x\) in the trinomial: \(3x^{2}+12x + x+4\).

Step3: Group and factor

Group the first two terms and the last two terms: \((3x^{2}+12x)+(x + 4)\). Factor out the greatest common factor from each group: \(3x(x + 4)+1(x + 4)\).

Step4: Factor out the common binomial

Factor out the common binomial \((x + 4)\): \((3x + 1)(x + 4)\).

Answer:

\((3x + 1)(x + 4)\)