Question

factor the trinomial.
v² + 3v − 54

select the correct choice below and fill in any answer boxes within your choice.
a. v² + 3v − 54 = \boxed{}
(type your answer in factored form. simplify your answer.)
b. the trinomial is not factorable.

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -54 and add up to 3. Let's list the factor pairs of -54: (-6, 9) because -6 * 9 = -54 and -6 + 9 = 3.

Step2: Factor the trinomial

Using the numbers -6 and 9, we can factor the trinomial \(v^2 + 3v - 54\) as \((v - 6)(v + 9)\) because when we expand \((v - 6)(v + 9)\), we get \(v^2 + 9v - 6v - 54 = v^2 + 3v - 54\), which matches the original trinomial.

Answer:

A. \(v^2 + 3v - 54 = (v - 6)(v + 9)\)