Question

factor the trinomial, or state that the trinomial is prime.
$5a^{2}-4a-28$
select the correct choice below and fill in any answer boxes within
a. $5a^{2}-4a-28=\square$
b. the polynomial is prime.

Explanation:

Step1: Find pair for product-sum

We need two numbers that multiply to $5\times(-28) = -140$ and add to $-4$. These numbers are $10$ and $-14$.

Step2: Split middle term

Rewrite the trinomial by splitting the linear term:
$5a^2 + 10a - 14a - 28$

Step3: Factor by grouping

Group terms and factor out common factors:
$5a(a + 2) - 14(a + 2)$

Step4: Factor out common binomial

Extract the shared binomial factor:
$(5a - 14)(a + 2)$

Answer:

A. $5a^{2}-4a-28=(5a-14)(a+2)$