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Factor. $\newline$ $2u^3 + 4u^2 + 9u + 18$

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Factor by grouping

Full solution

Q. Factor.

\newline

2u^3 + 4u^2 + 9u + 18

Identify Common Factors: Look for common factors in each pair of terms. $\newline$ We can pair the terms as $(2u^3 + 4u^2)$ and $(9u + 18)$ to look for common factors.
Factor First Pair: Factor out the common factor from the first pair of terms. $\newline$ The common factor in $2u^3$ and $4u^2$ is $2u^2$ . $\newline$ $2u^3 + 4u^2 = 2u^2(u + 2)$
Factor Second Pair: Factor out the common factor from the second pair of terms. $\newline$ The common factor in $9u$ and $18$ is $9$ . $\newline$ $9u + 18 = 9(u + 2)$
Write Down Findings: Write down what we have found so far. $\newline$ We have: $\newline$ $2u^3 + 4u^2 = 2u^2(u + 2)$ $\newline$ $9u + 18 = 9(u + 2)$ $\newline$ Now, we can see that $(u + 2)$ is a common factor.
Factor Entire Expression: Factor out the common factor $(u + 2)$ from the entire expression. $\newline$ We can write the original expression as: $\newline$ $2u^3 + 4u^2 + 9u + 18 = 2u^2(u + 2) + 9(u + 2)$ $\newline$ Now, factor out $(u + 2)$ : $\newline$ $2u^3 + 4u^2 + 9u + 18 = (u + 2)(2u^2 + 9)$

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