Question

factor the trinomial:
$3x^2 + 22x + 24$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $3\times24=72$ and add to 22: 18 and 4.
Rewrite the trinomial: $3x^2 + 18x + 4x + 24$

Step2: Group terms

Group the first two and last two terms: $(3x^2 + 18x) + (4x + 24)$

Step3: Factor out GCFs

Factor GCF from each group: $3x(x + 6) + 4(x + 6)$

Step4: Factor common binomial

Factor out $(x+6)$ from both terms: $(3x + 4)(x + 6)$

Answer:

$(3x + 4)(x + 6)$