College Algebra Question of the Day

1. $4ab(3b+4a)$ (correct answer)
2. $8ab(\,\frac{3}{2}b+2a)$
3. $4a(3b^2+4ab)$
4. $4b(3ab+4a^2)$

Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 12a b^2 + 16a^2 b, the GCF is 4a b, which, when factored out, results in the expression 4a b(3b + 4a). The correct choice, 4a b(3b+4a), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '4a($3b^2$+4a b)', which misses the common b. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.