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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $2u^3 + 6u^2$

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Factor out a monomial

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Q. Factor out the greatest common factor. If the greatest common factor is

1

, just retype the polynomial.

\newline

2u^3 + 6u^2

Identify GCF: Identify the greatest common factor (GCF) of the terms $2u^3$ and $6u^2$ . The common factors are $2$ , $u$ , and $u$ . $2 \times u \times u = 2u^2$ GCF of $2u^3$ and $6u^2$ : $2u^2$
Write $2u^3$ : Write $2u^3$ as the GCF times the remaining factors. $\newline$ $2u^3 = 2 \times u \times u \times u$ $\newline$ $2u^3 = 2u^2 \times u$
Write $6u^2$ : Write $6u^2$ as the GCF times the remaining factors. $\newline$ $6u^2 = 2 \times 3 \times u \times u$ $\newline$ $6u^2 = 2u^2 \times 3$
Combine terms: Combine the factored terms using the GCF. $\newline$ $2u^3 + 6u^2$ $\newline$ = $2u^2 \cdot u + 2u^2 \cdot 3$ $\newline$ = $2u^2(u + 3)$

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