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

Identify a, b, c: Identify a, b, and c in the quadratic expression 3f^2 + 11f + 6 by comparing it with the standard form ax^2 + bx + c. a = 3 b = 11 c = 6Find Multiplying Numbers: Find two numbers that multiply to a*c (3*6=18) and add up to b (11). We need to find two numbers that satisfy these conditions. After checking possible pairs that multiply to 18 (such as 1 and 18, 2 and 9, 3 and 6), we find that 2 and 9 are the numbers we are looking for because 2*9=18 and 2+9=11.Rewrite Middle Term: Rewrite the middle term, 11f, using the two numbers we found, 2 and 9, to split it into two terms. 3f^2 + 11f + 6 can be rewritten as 3f^2 + 2f + 9f + 6.Factor by Grouping: Factor by grouping. Group the first two terms together and the last two terms together. (3f^2 + 2f) + (9f + 6) Now factor out the common factors from each group. The common factor in the first group is f, and in the second group, it is 3. f(3f + 2) + 3(3f + 2)Factor out Common Factor: Notice that (3f + 2) is a common factor in both groups. Factor out (3f + 2). The factored form is (f + 3)(3f + 2).

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Factor. $\newline$ $3f^2 + 11f + 6$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

\newline

3f^2 + 11f + 6

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3f^2 + 11f + 6$ by comparing it with the standard form $ax^2 + bx + c$ .
$a = 3$
$b = 11$
$b$ $0$
Find Multiplying Numbers: Find two numbers that multiply to $a*c$ ( $3*6=18$ ) and add up to $b$ ( $11$ ). $\newline$ We need to find two numbers that satisfy these conditions. $\newline$ After checking possible pairs that multiply to $18$ (such as $1$ and $18$ , $2$ and $9$ , $3$ and $3*6=18$ $0$ ), we find that $2$ and $9$ are the numbers we are looking for because $3*6=18$ $3$ and $3*6=18$ $4$ .
Rewrite Middle Term: Rewrite the middle term, $11f$ , using the two numbers we found, $2$ and $9$ , to split it into two terms. $\newline$ $3f^2 + 11f + 6$ can be rewritten as $3f^2 + 2f + 9f + 6$ .
Factor by Grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(3f^2 + 2f) + (9f + 6)$ $\newline$ Now factor out the common factors from each group. $\newline$ The common factor in the first group is $f$ , and in the second group, it is $3$ . $\newline$ $f(3f + 2) + 3(3f + 2)$
Factor out Common Factor: Notice that $3f + 2$ is a common factor in both groups. Factor out $3f + 2$ . The factored form is $f + 3$ $(3f + 2)$ .