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Question

# Completely factor this trinomial. Prior to factoring, first write the trinomial in decreasing powers.$14 a^2 b^3+15 a b^3-9 b^3$

Solution

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We must factor completely the given polynomial:

$14a^2b^3 + 15ab^3 - 9b^3$

First, factor out the greatest common factor $(GCF)$:

To find the greatest common factor, first factor the terms:

\begin{align*} 14a^2b^3&= b^3\cdot 14 \cdot a^2\\ 15ab^3&=b^3 \cdot 15 \cdot a \\ 9b^3&=b^3\cdot 9 \end{align*}

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