Question

factor the trinomial:
$5x^2 + 32x + 12$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $5\times12=60$ and add to 32. These numbers are 30 and 2.
Rewrite the trinomial: $5x^2 + 30x + 2x + 12$

Step2: Group terms

Group the first two and last two terms: $(5x^2 + 30x) + (2x + 12)$

Step3: Factor out GCFs

Factor $5x$ from first group, 2 from second: $5x(x + 6) + 2(x + 6)$

Step4: Factor common binomial

Factor out $(x + 6)$: $(5x + 2)(x + 6)$

Answer:

$(5x + 2)(x + 6)$