Question

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) Marisol noticed that she does not have a common factor. Which accurately describes what Marisol should do next? Marisol should realize that her work shows that the polynomial is prime. Marisol should go back and group the terms in Step 1 as (6x3 – 22x2) – (9x – 33). Marisol should go back and group the terms in Step 1 as (6x3 – 22x2) + (9x – 33). Marisol should refactor the expression in Step 2 as 2x2(3x + 11) – 3(3x + 11).

Answer 1

Answer:

Marisol should go back and group the terms in Step 1 as (6x³ – 22x²) – (9x – 33)

Step-by-step explanation:

Given the polynomial factorized by Marisol given as 6x³ – 22x² – 9x + 33. To factor out the common GCF out of the group, the following steps should have been taken by Marisol.

Step 1: Regroup into parts using parenthesis

(6x³ – 22x²) – (9x - 33)

Note that when regrouping -9x+33, the positive sign inside the parenthesis will change to negative and that was Marisol's error according to her calculation.

Step 2: Factor out the common terms in both parenthesis

2x²(3x – 11) – 3(3x - 11)

(2x²-3)(3x-11)

Based on the calculation, the statement that accurately describes what Marisol should do next is that Marisol should go back and group the terms in Step 1 as (6x³– 22x²) – (9x – 33)