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Factor. $\newline$ $7y^3 + 14y^2 + 9y + 18$

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Factor by grouping

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Q. Factor.

\newline

7y^3 + 14y^2 + 9y + 18

Identify Common Factors: Look for common factors in each pair of terms. $\newline$ We can group the terms as $(7y^3 + 14y^2)$ and $(9y + 18)$ to look for common factors within each group.
Factor First Group: Factor out the common factor from the first group. $\newline$ The common factor in the first group $7y^3 + 14y^2$ is $7y^2$ . $\newline$ $7y^3 + 14y^2 = 7y^2(y + 2)$
Factor Second Group: Factor out the common factor from the second group. $\newline$ The common factor in the second group $9y + 18$ is $9$ . $\newline$ $9y + 18 = 9(y + 2)$
Write Factored Form: Write the factored form of the entire expression. $\newline$ Now we have: $\newline$ $7y^3 + 14y^2 + 9y + 18 = 7y^2(y + 2) + 9(y + 2)$ $\newline$ Notice that $(y + 2)$ is a common factor in both terms.
Factor Out Common Factor: Factor out the common factor $(y + 2)$ . $\newline$ Factor out $(y + 2)$ from both terms. $\newline$ $7y^3 + 14y^2 + 9y + 18 = (y + 2)(7y^2 + 9)$
Check for Further Factoring: Check if the second factor $(7y^2 + 9)$ can be factored further. $\newline$ The second factor $(7y^2 + 9)$ does not have a common factor and is not a difference of squares, so it cannot be factored further.

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