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Factor. $\newline$ $8m^3 + 16m^2 - 9m - 18$

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Factor by grouping

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Q. Factor.

\newline

8m^3 + 16m^2 - 9m - 18

Grouping for Factoring: Group the terms into two pairs to prepare for factoring by grouping. Group the first two terms and the last two terms separately. $8m^3 + 16m^2$ + $-9m - 18$
Factor out Common Factors: Factor out the greatest common factor from each group. $\newline$ From the first group, factor out $8m^2$ . From the second group, factor out $-9$ . $\newline$ $8m^2(m + 2) - 9(m + 2)$
Common Factor Product: Notice that $(m + 2)$ is a common factor in both groups. $\newline$ Write the expression as a product of $(m + 2)$ and another factor. $\newline$ $(8m^2 - 9)(m + 2)$
Further Factoring: Check if the factors can be factored further. $\newline$ The factor $8m^2 - 9$ is a difference of squares and can be factored further. $\newline$ $(2m)^2 - (3)^2 = (2m + 3)(2m - 3)$
Final Factored Form: Write the final factored form of the original expression. $\newline$ $(2m + 3)(2m - 3)(m + 2)$

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