Factor. 3m^2 + 11m + 6 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 3m^2 + 11m + 6 by comparing it with the standard form ax^2 + bx + c. a = 3 b = 11 c = 6Find two numbers: Find two numbers that multiply to a*c (3*6 = 18) and add up to b (11). The two numbers that satisfy these conditions are 2 and 9 because: 2 * 9 = 18 2 + 9 = 11Rewrite middle term: Rewrite the middle term, 11m, using the two numbers found in the previous step. 3m^2 + 11m + 6 can be rewritten as: 3m^2 + 2m + 9m + 6Group and factor: Group the terms into two pairs and factor by grouping. Group (3m^2 + 2m) and (9m + 6). Factor out the greatest common factor from each group: From (3m^2 + 2m), factor out m: m(3m + 2) From (9m + 6), factor out 3: 3(3m + 2)Factor out common factor: Now that we have a common factor of (3m + 2) in both groups, factor out (3m + 2). The expression becomes: (3m + 2)(m + 3)

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3m^2 + 11m + 6

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3m^2 + 11m + 6$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 3$ $\newline$ $b = 11$ $\newline$ $b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ ( $3*6 = 18$ ) and add up to $b$ ( $11$ ). $\newline$ The two numbers that satisfy these conditions are $2$ and $9$ because: $\newline$ $2 * 9 = 18$ $\newline$ $2 + 9 = 11$
Rewrite middle term: Rewrite the middle term, $11m$ , using the two numbers found in the previous step. $\newline$ $3m^2 + 11m + 6$ can be rewritten as: $\newline$ $3m^2 + 2m + 9m + 6$
Group and factor: Group the terms into two pairs and factor by grouping. $\newline$ Group $(3m^2 + 2m)$ and $(9m + 6)$ . $\newline$ Factor out the greatest common factor from each group: $\newline$ From $(3m^2 + 2m)$ , factor out $m$ : $m(3m + 2)$ $\newline$ From $(9m + 6)$ , factor out $3$ : $3(3m + 2)$
Factor out common factor: Now that we have a common factor of $(3m + 2)$ in both groups, factor out $(3m + 2)$ . The expression becomes: $(3m + 2)(m + 3)$