Multiple Choice
Factor the GCF out of:
7. Factoring
Factoring by Greatest Common Factor & Grouping
Multiple Choice
Use grouping to factor out the polynomial.
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Verified step by step guidance1
Group the polynomial into two pairs to make factoring easier: group the first two terms and the last two terms separately. So, write it as \(\left(2ab + 4a\right) + \left(3b^2 + 6b\right)\).
Factor out the greatest common factor (GCF) from each group. From the first group \(2ab + 4a\), factor out \$2a\( to get \(2a(b + 2)\). From the second group \(3b^2 + 6b\), factor out \)3b$ to get \(3b(b + 2)\).
Notice that both groups now contain the common binomial factor \((b + 2)\). This is key to factoring by grouping.
Factor out the common binomial factor \((b + 2)\) from the entire expression, which gives you \((b + 2)(2a + 3b)\).
Verify your factorization by expanding the factors back out to ensure it matches the original polynomial.
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