Question

question
factor the trinomial:

$3x^2 + 22x + 24$

answer
attempt 1 out of 2

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Explanation:

Step1: Find product of leading coefficient and constant

$3 \times 24 = 72$

Step2: Identify pair summing to 22

We need two numbers that multiply to 72 and add to 22: 18 and 4, since $18 \times 4 = 72$ and $18 + 4 = 22$.

Step3: Split middle term

Rewrite the trinomial by splitting the $22x$ term:
$3x^2 + 18x + 4x + 24$

Step4: Factor by grouping

Group the first two and last two terms, then factor out the GCF from each group:
$3x(x + 6) + 4(x + 6)$

Step5: Factor out common binomial

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

Answer:

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