582
RCMultiple Choice

Unit Summary — Cumulative exam

Question 582 • Career Explorations - EL3401

Marisol grouped the terms and factored the GCF out of the groups of the polynomial 6x3 – 22x2 – 9x + 33. Her work is shown.Step 1: (6x3 – 22x2) – (9x + 33)Step 2: 2x2(3x – 11) – 3(3x + 11)

Answer
A
Marisol should realize that her work shows that the polynomial is prime.
B
Marisol should go back and group the terms in Step 1 as (6x3 – 22x2) – (9x – 33).
C
Marisol should go back and group the terms in Step 1 as (6x3 – 22x2) + (9x – 33).
D
Marisol should refactor the expression in Step 2 as 2x2(3x + 11) – 3(3x + 11).

Explanation

The last two terms of the polynomial are −9x + 33. To group them using subtraction, write −(9x − 33), since distributing the minus gives −9x + 33. So Step 1 should be (6x³ − 22x²) − (9x − 33), which factors as 2x²(3x − 11) − 3(3x − 11). Both groups then share the factor 3x − 11.

AI-written and checked against the verified answer.

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