Factor. 2n^2 + 11n + 9 ____

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

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Factor. $\newline$ $2n^2 + 11n + 9$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2n^2 + 11n + 9

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