Question

question
factor the trinomial:
$3x^2 + 22x + 7$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times7 = 21\) and add up to \(22\). The numbers are \(21\) and \(1\) since \(21\times1 = 21\) and \(21 + 1=22\).

Step2: Rewrite the middle term

Rewrite the trinomial \(3x^{2}+22x + 7\) as \(3x^{2}+21x+x + 7\).

Step3: Group the terms

Group the first two terms and the last two terms: \((3x^{2}+21x)+(x + 7)\).

Step4: Factor out the GCF from each group

Factor out \(3x\) from the first group and \(1\) from the second group: \(3x(x + 7)+1(x + 7)\).

Step5: Factor out the common binomial factor

Factor out \((x + 7)\) from both terms: \((3x + 1)(x + 7)\).

Answer:

\((3x + 1)(x + 7)\)