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Factor. $\newline$ $3m^2 + 5m + 2$

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Factor quadratics with other leading coefficients

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Q. Factor.

\newline

3m^2 + 5m + 2

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3m^2 + 5m + 2$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 3$ $\newline$ $b = 5$ $\newline$ $b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $3*2=6$ ) and add up to $b$ (which is $5$ ). $\newline$ The two numbers that satisfy these conditions are $2$ and $3$ because: $\newline$ $2 * 3 = 6$ $\newline$ $2 + 3 = 5$
Rewrite middle term: Rewrite the middle term, $5m$ , using the two numbers found in the previous step to split it into two terms. $\newline$ $3m^2 + 5m + 2$ can be rewritten as: $\newline$ $3m^2 + 2m + 3m + 2$
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together, then factor out the common factor from each group. $\newline$ From $3m^2 + 2m$ , factor out $m$ : $\newline$ $m(3m + 2)$ $\newline$ From $3m + 2$ , factor out $1$ : $\newline$ $1(3m + 2)$ $\newline$ Now we have: $\newline$ $m(3m + 2) + 1(3m + 2)$
Factor out common binomial: Factor out the common binomial factor $(3m + 2)$ from both groups. $\newline$ $(3m + 2)(m + 1)$

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