Final answer:
The correct term to use in the blank of 3662-222 to ensure the resulting polynomial's GCF is 2 is option c. 24, as it maintains 2 as the greatest common factor without introducing higher powers of 2.
Step-by-step explanation:
The question asks which term can be used in the blank of 3662−222 so the greatest common factor (GCF) of the resulting polynomial is 2. To find this term, we need to consider the prime factorization of both terms in the polynomial. The prime factorization of 3662 is 2×1831, and the prime factorization of the second term would be 2×… because we want the GCF to be 2. Since the term -222 in the polynomial already has 2 as a factor, to maintain a GCF of 2 we need the blank term to also have a single factor of 2 and no higher powers of 2. This rules out options a, b, and d because 12, 18, and 36 have factors of 2 raised to a power higher than 1. So, the correct answer is option c. 24, which has a prime factorization of 2^3×3, ensuring the resulting polynomial maintains 2 as its greatest common factor.