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

Identify a, b, c: Identify a, b, and c in the quadratic expression 3n^2 + 11n + 6. Compare 3n^2 + 11n + 6 with the standard form ax^2 + bx + c. a = 3 b = 11 c = 6Find Numbers Multiply Add: Find two numbers that multiply to a*c (which is 3*6=18) and add up to b (which is 11). The two numbers that satisfy these conditions are 2 and 9 because 2*9 = 18 and 2+9 = 11.Rewrite Middle Term: Rewrite the middle term 11n using the two numbers found in Step 2. 3n^2 + 11n + 6 can be rewritten as 3n^2 + 2n + 9n + 6.Factor by Grouping: Factor by grouping. Group the terms into two pairs: (3n^2 + 2n) and (9n + 6). Factor out the greatest common factor from each pair. From 3n^2 + 2n, factor out n to get n(3n + 2). From 9n + 6, factor out 3 to get 3(3n + 2).Write Factored Form: Write the factored form of the expression. Since both groups contain the factor (3n + 2), factor this out to get: (n + 3)(3n + 2)

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3n^2 + 11n + 6

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3n^2 + 11n + 6$ . Compare $3n^2 + 11n + 6$ with the standard form $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find Numbers Multiply Add: Find two numbers that multiply to $a*c$ (which is $3*6=18$ ) and add up to $b$ (which is $11$ ). $\newline$ The two numbers that satisfy these conditions are $2$ and $9$ because $2*9 = 18$ and $2+9 = 11$ .
Rewrite Middle Term: Rewrite the middle term $11n$ using the two numbers found in Step $2$ . $\newline$ $3n^2 + 11n + 6$ can be rewritten as $3n^2 + 2n + 9n + 6$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $(3n^2 + 2n)$ and $(9n + 6)$ . $\newline$ Factor out the greatest common factor from each pair. $\newline$ From $3n^2 + 2n$ , factor out $n$ to get $n(3n + 2)$ . $\newline$ From $9n + 6$ , factor out $3$ to get $3(3n + 2)$ .
Write Factored Form: Write the factored form of the expression. $\newline$ Since both groups contain the factor $(3n + 2)$ , factor this out to get: $\newline$ $(n + 3)(3n + 2)$