Question

factor the trinomial.
w² + 11w + 24

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

○ a. the answer is
○ b. the trinomial is not factorable.

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(24\) (the constant term) and add up to \(11\) (the coefficient of the middle term). Let's list the factor pairs of \(24\): \(1\) and \(24\) (sum \(25\)), \(2\) and \(12\) (sum \(14\)), \(3\) and \(8\) (sum \(11\)), \(4\) and \(6\) (sum \(10\)). So the numbers are \(3\) and \(8\).

Step2: Factor the trinomial

Using the numbers \(3\) and \(8\), we can factor the trinomial \(w^{2}+11w + 24\) as \((w + 3)(w+8)\).

Answer:

A. The answer is \((w + 3)(w + 8)\)