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Factor. $\newline$ $6f^3 + 3f^2 + 2f + 1$

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Factor by grouping

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Q. Factor.

\newline

6f^3 + 3f^2 + 2f + 1

Identify Common Factors: Look for common factors in each pair of terms. We can pair the terms as $6f^3 + 3f^2$ and $2f + 1$ to look for common factors.
Factor Out First Pair: Factor out the common factor from the first pair of terms. $\newline$ The common factor in $6f^3$ and $3f^2$ is $3f^2$ . $\newline$ $6f^3 + 3f^2 = 3f^2(2f + 1)$
Factor Out Second Pair: Factor out the common factor from the second pair of terms. $\newline$ The second pair of terms, $2f + 1$ , does not have a common factor other than $1$ . $\newline$ $2f + 1 = 1(2f + 1)$
Find Common Binomial Factor: Look for a common binomial factor in the expressions found in Step $2$ and Step $3$ . $\newline$ Both $3f^2(2f + 1)$ and $1(2f + 1)$ have a common binomial factor of $(2f + 1)$ .
Factor Out Common Binomial Factor: Factor out the common binomial factor. $\newline$ The factored form of the polynomial is $(2f + 1)(3f^2 + 1)$ .

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