Question

question
factor the trinomial:
2x² + 9x + 7

Explanation:

Step1: Multiply leading - coefficient and constant

Multiply 2 and 7, we get $2\times7 = 14$.

Step2: Find two numbers for 14

We need two numbers that multiply to 14 and add up to 9. The numbers are 2 and 7 since $2\times7=14$ and $2 + 7=9$.

Step3: Rewrite middle term

Rewrite $9x$ as $2x+7x$. So the trinomial becomes $2x^{2}+2x + 7x+7$.

Step4: Group terms

Group the terms: $(2x^{2}+2x)+(7x + 7)$.

Step5: Factor out GCF from each group

From the first group $2x^{2}+2x$, the GCF is $2x$, so we have $2x(x + 1)$. From the second group $7x+7$, the GCF is 7, so we have $7(x + 1)$.

Step6: Factor out common binomial

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

Answer:

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