Factor the four-term polynomial by grouping.
-$20 a ^ { 3 } + 15 a ^ { 2 } b + 24 a b ^ { 2 } + 18 b ^ { 3 }$
A) $\left( 20 a ^ { 2 } + 6 b ^ { 2 } \right) ( a + 3 b )$
B) $\left( 5 a ^ { 2 } - 6 b ^ { 2 } \right) ( 4 a - 3 b )$
C) $\left( 5 a ^ { 2 } + 6 b \right) ( 4 a + 3 b )$
D) $\left( 5 a ^ { 2 } + 6 b ^ { 2 } \right) ( 4 a + 3 b )$

Question

Quizplus · Accepted Answer

To factor the given polynomial by grouping, we first group the terms: $20a^3 + 15a^2b$ and $24ab^2 + 18b^3$. Factoring out the greatest common factor from each group gives us $5a^2(4a + 3b) + 6b^2(4a + 3b)$. We can then factor out the common factor $(4a + 3b)$, resulting in $(5a^2 + 6b^2)(4a + 3b)$, which matches option D.

Factor the Four-Term Polynomial by Grouping 20a3+15a2b+24ab2+18b320 a ^ { 3 } + 15 a ^ { 2 } b + 24 a b ^ { 2 } + 18 b ^ { 3 }20a3+15a2b+24ab2+18b3

Factor the Four-Term Polynomial by Grouping $20 a ^ { 3 } + 15 a ^ { 2 } b + 24 a b ^ { 2 } + 18 b ^ { 3 }$