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

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Factor by grouping

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Q. Factor.

\newline

2n^3 + n^2 + 16n + 8

Group terms for factoring: Look for common factors in pairs of terms. $\newline$ We will first group the terms into pairs to see if we can factor by grouping. $\newline$ Group the first two terms and the last two terms: $(2n^3 + n^2) + (16n + 8)$ .
Factor first group: Factor out the greatest common factor from the first group. $\newline$ The greatest common factor of $2n^3$ and $n^2$ is $n^2$ . $\newline$ Factor out $n^2$ : $n^2(2n + 1)$ .
Factor second group: Factor out the greatest common factor from the second group. $\newline$ The greatest common factor of $16n$ and $8$ is $8$ . $\newline$ Factor out $8$ : $8(2n + 1)$ .
Write factored polynomial: Write the factored form of the polynomial. $\newline$ We have factored both groups and found a common binomial factor $(2n + 1)$ . $\newline$ Combine the factored groups: $(n^2 + 8)(2n + 1)$ .

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