Use grouping to factor out the polynomial.
$2ab+4a+3b^2+6b$

• A. $(2a+3)(b+2)$
• B. $(2a+b)(b+6)$
• C. $(b+2)(2a+3b)$
• D. $(a+3b)(2b+2)$

Answer: (C)

Verified step by step guidance

1. Start with the polynomial: \$2ab + 4a + 3b^{2} + 6b$.
2. Group the terms in pairs to make factoring easier: \((2ab + 4a) + (3b^{2} + 6b)\).
3. Factor out the greatest common factor (GCF) from each group: from the first group, factor out \$2a\( to get \)2a(b + 2)\(; from the second group, factor out \)3b\( to get \)3b(b + 2)$.
4. Notice that both groups now contain the common binomial factor \((b + 2)\), so factor this out: \((b + 2)(2a + 3b)\).
5. The polynomial is now factored completely as the product of two binomials: \((b + 2)(2a + 3b)\).