QuestionJuly 26, 2025

Question 5(Multiple Choice Worth 4 points) (07.01, 07.02 MC) Factor the greatest common factor: 9a^4b^3+24a^3b^2-15a^2b 3a^2b(3a^2b^2+8ab-5) 3a^2b^3(3a^2+8ab-5) 3a^2b(3a^2b+8ab-5b) 3ab(3a^3b^2+8ab-5a)

Question 5(Multiple Choice Worth 4 points) (07.01, 07.02 MC) Factor the greatest common factor: 9a^4b^3+24a^3b^2-15a^2b 3a^2b(3a^2b^2+8ab-5) 3a^2b^3(3a^2+8ab-5) 3a^2b(3a^2b+8ab-5b) 3ab(3a^3b^2+8ab-5a)
Question 5(Multiple Choice Worth 4 points) (07.01, 07.02 MC) Factor the greatest common factor: 9a^4b^3+24a^3b^2-15a^2b 3a^2b(3a^2b^2+8ab-5) 3a^2b^3(3a^2+8ab-5) 3a^2b(3a^2b+8ab-5b) 3ab(3a^3b^2+8ab-5a)

Solution
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Answer

3a^{2}b(3a^{2}b^{2}+8ab-5) Explanation 1. Identify the Greatest Common Factor (GCF) The GCF of 9a^{4}b^{3}, 24a^{3}b^{2}, and 15a^{2}b is 3a^{2}b. 2. Factor out the GCF Divide each term by 3a^{2}b: - 9a^{4}b^{3} \div 3a^{2}b = 3a^{2}b^{2} - 24a^{3}b^{2} \div 3a^{2}b = 8ab - 15a^{2}b \div 3a^{2}b = 5 3. Write the Factored Expression Combine the results: 3a^{2}b(3a^{2}b^{2} + 8ab - 5)

Explanation

1. Identify the Greatest Common Factor (GCF)<br /> The GCF of $9a^{4}b^{3}$, $24a^{3}b^{2}$, and $15a^{2}b$ is $3a^{2}b$.<br /><br />2. Factor out the GCF<br /> Divide each term by $3a^{2}b$: <br />- $9a^{4}b^{3} \div 3a^{2}b = 3a^{2}b^{2}$<br />- $24a^{3}b^{2} \div 3a^{2}b = 8ab$<br />- $15a^{2}b \div 3a^{2}b = 5$<br /><br />3. Write the Factored Expression<br /> Combine the results: $3a^{2}b(3a^{2}b^{2} + 8ab - 5)$
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