Question

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

Marisol did a mistake while grouping the terms in Step 1, with the sign. Thus, Marisol should go back and group the terms in Step 1 as (6x³ - 22x²) - (9x - 33). Hence, the second option is the correct choice.

The polynomial Marisol had was 6x³ - 22x² - 9x + 33.

The steps she did in the grouping of terms and factoring out the GFC out of the groups were:

Step 1: (6x³ - 22x²) - (9x + 33).

Step 2: 2x²(3x - 11) -3(3x + 11).

After this Marisol was unable to get a common factor to proceed further.

The mistake that Marisol did was in Step 1, as while grouping -9x and +33, she took the minus sign out, which will make -9x to become 9x, but 33 to become -33.

This is where she made the mistake and writing - (9x + 33) in place of - (9x - 33).

Thus, her steps should have been:

Step 1: (6x³ - 22x) - (9x - 33),

Step 2: 2x²(3x - 11) -3(3x - 11), which gives her a common factor (3x - 11), to continue with the third step:

Step 3: (2x² - 3)(3x - 11).

Refer to the attachment for the complete question, as the given question is incomplete.

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