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

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Factor by grouping

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Q. Factor.

\newline

16n^3 + 8n^2 + 18n + 9

Identify Common Factors: Look for common factors in the first two terms and the last two terms separately. $\newline$ For the first two terms, $16n^3$ and $8n^2$ , the common factor is $8n^2$ . $\newline$ For the last two terms, $18n$ and $9$ , the common factor is $9$ .
Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms. $\newline$ $16n^3 + 8n^2 = 8n^2(2n + 1)$ $\newline$ $18n + 9 = 9(2n + 1)$
Factor Out Common Binomial: Now, we have two expressions $8n^2(2n + 1)$ and $9(2n + 1)$ which share a common binomial factor $(2n + 1)$ . Factor out the common binomial factor $(2n + 1)$ . So, the factored form of $16n^3 + 8n^2 + 18n + 9$ is $(2n + 1)(8n^2 + 9)$ .

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