Question

question
factor the trinomial:
$2x^2 + 9x + 7$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $2\times7=14$ and add to $9$. The numbers are $2$ and $7$. Rewrite the trinomial:
$2x^2 + 2x + 7x + 7$

Step2: Group terms

Group the first two and last two terms:
$(2x^2 + 2x) + (7x + 7)$

Step3: Factor out GCFs

Factor out the greatest common factor from each group:
$2x(x + 1) + 7(x + 1)$

Step4: Factor common binomial

Factor out the shared binomial $(x+1)$:
$(2x + 7)(x + 1)$

Answer:

$(2x + 7)(x + 1)$