Question

factor the following trinomial.
$4x^2 + 23x - 35$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. $4x^2 + 23x - 35 = \square$

b. the polynomial is prime.

Explanation:

Step1: Split middle term

Find two numbers that multiply to $4\times(-35)=-140$ and add to 23. These numbers are 28 and -5.
Rewrite the trinomial: $4x^2 + 28x - 5x - 35$

Step2: Group terms

Group the first two and last two terms: $(4x^2 + 28x) + (-5x - 35)$

Step3: Factor out GCFs

Factor GCF from each group: $4x(x + 7) - 5(x + 7)$

Step4: Factor common binomial

Factor out $(x+7)$ from both terms: $(4x - 5)(x + 7)$

Answer:

A. $4x^{2}+23x-35=(4x-5)(x+7)$