7
QuizMultiple Choice

Factoring Trinomials: a > 1 — Unit test

Question 7 • FL-1200700-Mathematics for College Algebra MIS

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)

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

Explanation

The first group factors as 3x²(x − 5). The second group, −4x + 20, should be factored as −4(x − 5), so both groups have the same binomial factor. Omar’s 4(−x + 5) is equivalent, but factoring out a negative makes the shared factor clear; the polynomial then factors as (3x² − 4)(x − 5).

AI-written and checked against the verified answer.

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