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 numbers multiply and add: 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. After checking possible pairs that multiply to 18 (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 = 11.Rewrite middle term: Rewrite the middle term 11n using the two numbers found in Step 2. We can express 11n as the sum of 2n and 9n. 2n^2 + 11n + 9 becomes 2n^2 + 2n + 9n + 9.Factor by grouping: Factor by grouping. First, group the terms: (2n^2 + 2n) + (9n + 9). Now, factor out the common factors from each group. From the first group, we can factor out 2n: 2n(n + 1). From the second group, we can factor out 9: 9(n + 1).Write factored form: Write the factored form of the expression. Since both groups contain the common factor (n + 1), we can 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 numbers multiply and add: 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 $11$ . $\newline$ After checking possible pairs that multiply to $18$ ( $1$ and $18$ , $2$ and $2*9 = 18$ $0$ , $2*9 = 18$ $1$ and $2*9 = 18$ $2$ ), we find that $2$ and $2*9 = 18$ $0$ are the numbers we are looking for because $2*9 = 18$ $5$ .
Rewrite middle term: Rewrite the middle term $11n$ using the two numbers found in Step $2$ . $\newline$ We can express $11n$ as the sum of $2n$ and $9n$ . $\newline$ $2n^2 + 11n + 9$ becomes $2n^2 + 2n + 9n + 9$ .
Factor by grouping: Factor by grouping. $\newline$ First, group the terms: $2n^2 + 2n$ + $9n + 9$ . $\newline$ Now, factor out the common factors from each group. $\newline$ From the first group, we can factor out $2n$ : $2n(n + 1)$ . $\newline$ From the second group, we can factor out $9$ : $9(n + 1)$ .
Write factored form: Write the factored form of the expression. $\newline$ Since both groups contain the common factor $(n + 1)$ , we can factor this out. $\newline$ The factored form is $(2n + 9)(n + 1)$ .