Question

Omar grouped the terms and factored the GCF out of the groups of the polynomial 3x3 – 15x2 – 4x + 20. His work is shown.

Step 1: (3x3 – 15x2) + (–4x + 20)

Step 2: 3x2(x – 5) + 4(–x + 5)

Omar noticed that he does not have a common factor. Which accurately describes what Omar should do next?

Omar should realize that his work shows that the polynomial is prime.
Omar should go back and regroup the terms in Step 1 as (3x3 – 15x2) – (4x + 20).
In Step 2, Omar should factor only out of the first expression.
Omar should factor out a negative from one of the groups so the binomials will be the same.

Answer 1

Omar should factor out a negative from one of the groups so the binomials will be the same.

Reason: 3x^2(x − 5) + 4(−x + 5) = 3x^2(x − 5) − 4(x − 5) (since 4(−x + 5) = −4(x − 5)).
Now factor (x − 5): (x − 5)(3x^2 − 4).