Question

factor the trinomial.
3s² - 33s + 84
select the correct choice below and, if necessary, fill in the answer box within your choice.
○ a. the answer is . (factor completely.)
○ b. the trinomial is not factorable.

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(3s^2\), \(-33s\), and \(84\) is \(3\). So we factor out \(3\) from the trinomial:
\(3s^2 - 33s + 84 = 3(s^2 - 11s + 28)\)

Step2: Factor the quadratic inside the parentheses

We need to find two numbers that multiply to \(28\) (the constant term) and add up to \(-11\) (the coefficient of the middle term). The numbers \(-4\) and \(-7\) satisfy this because \((-4)\times(-7)=28\) and \(-4 + (-7)=-11\). So we can factor \(s^2 - 11s + 28\) as \((s - 4)(s - 7)\).

Putting it all together, the factored form of the trinomial is \(3(s - 4)(s - 7)\).

Answer:

A. The answer is \(3(s - 4)(s - 7)\). (Factor completely.)