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Factor. $\newline$ $3f^2 + 8f + 4$

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Factor quadratics with other leading coefficients

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Q. Factor.

\newline

3f^2 + 8f + 4

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3f^2 + 8f + 4$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 3$ $\newline$ $b = 8$ $\newline$ $b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $3*4=12$ ) and add up to $b$ (which is $8$ ). $\newline$ The two numbers that satisfy these conditions are $2$ and $6$ because: $\newline$ $2 \times 6 = 12$ $\newline$ $2 + 6 = 8$
Rewrite middle term: Rewrite the middle term, $8f$ , using the two numbers found in the previous step. $\newline$ $3f^2 + 8f + 4$ can be rewritten as $3f^2 + 2f + 6f + 4$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(3f^2 + 2f) + (6f + 4)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ The greatest common factor of $3f^2$ and $2f$ is $f$ , so factor out $f$ from the first group: $\newline$ $f(3f + 2)$ $\newline$ The greatest common factor of $6f$ and $4$ is $2$ , so factor out $2$ from the second group: $\newline$ $2(3f + 2)$
Factor out common factor: Notice that both groups contain the common factor $(3f + 2)$ . Factor out $(3f + 2)$ from the expression. $f(3f + 2) + 2(3f + 2)$ can be factored as $(3f + 2)(f + 2)$ .

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