Question

factor the trinomial: $2x^{2}+19x+42$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $2\times42=84$ and add to 19. These numbers are 12 and 7. Rewrite the trinomial:
$2x^2 + 12x + 7x + 42$

Step2: Group and factor pairs

Group the first two and last two terms, then factor out the GCF from each group:
$2x(x + 6) + 7(x + 6)$

Step3: Factor out common binomial

Factor out the shared binomial $(x + 6)$:
$(2x + 7)(x + 6)$

Answer:

$(2x + 7)(x + 6)$