which term can be used in the blank of 36x³ - 22x² - __ so the greatest common factor of the resulting…

Explanation:

Step1: Analyze the GCF of given terms

The GCF of (36x^{3}) and (- 22x^{2}) should have factors that can also divide the third - term for the overall GCF to be (2x). The GCF of (36x^{3}) and (-22x^{2}) already has a factor of (2x). We need to check which of the options has (2x) as a factor.

Step2: Check option 1

For (2), the GCF of (36x^{3},-22x^{2},2) is (2), not (2x) since (2) does not have (x) as a factor.

Step3: Check option 2

For (4xy), we can factor out (2x) from (4xy) ((4xy = 2x\times2y)). Also, (36x^{3}=2x\times18x^{2}) and (-22x^{2}=2x\times(- 11x)).

Step4: Check option 3

For (12x), we can factor out (2x) from (12x) ((12x = 2x\times6)). Also, (36x^{3}=2x\times18x^{2}) and (-22x^{2}=2x\times(-11x)).

Step5: Check option 4

For (24), the GCF of (36x^{3},-22x^{2},24) is (2), not (2x) since (24) does not have (x) as a factor.

Step6: Check option 5

For (44y), the GCF of (36x^{3},-22x^{2},44y) is (2), not (2x) since (44y) does not have (x) as a factor.

Answer:

B. (4xy), C. (12x)