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

Identify a, b, c: Identify a, b, and c in the quadratic expression 2f^2 + 11f + 9. Compare 2f^2 + 11f + 9 with ax^2 + bx + c. a = 2 b = 11 c = 9Find numbers multiply 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 of factors of 18 (1 and 18, 2 and 9, 3 and 6), we find that 2 and 9 are the correct pair because 2 + 9 = 11.Rewrite middle term: Rewrite the middle term 11f using the two numbers found in Step 2. The expression 2f^2 + 11f + 9 can be rewritten by splitting the middle term into 2f and 9f. 2f^2 + 11f + 9 = 2f^2 + 2f + 9f + 9Factor by grouping: Factor by grouping. First, group the terms: (2f^2 + 2f) + (9f + 9). Now, factor out the common factors from each group. From the first group, factor out 2f: 2f(f + 1). From the second group, factor out 9: 9(f + 1).Factor out common binomial: Factor out the common binomial (f + 1). We have 2f(f + 1) + 9(f + 1). Factor out the common binomial (f + 1) to get (f + 1)(2f + 9).

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

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2f^2 + 11f + 9

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2f^2 + 11f + 9$ . Compare $2f^2 + 11f + 9$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find numbers multiply 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 of factors of $18$ ( $1$ 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 correct pair because $2*9 = 18$ $5$ .
Rewrite middle term: Rewrite the middle term $11f$ using the two numbers found in Step $2$ . $\newline$ The expression $2f^2 + 11f + 9$ can be rewritten by splitting the middle term into $2f$ and $9f$ . $\newline$ $2f^2 + 11f + 9 = 2f^2 + 2f + 9f + 9$
Factor by grouping: Factor by grouping. $\newline$ First, group the terms: $2f^2 + 2f$ + $9f + 9$ . $\newline$ Now, factor out the common factors from each group. $\newline$ From the first group, factor out $2f$ : $2f(f + 1)$ . $\newline$ From the second group, factor out $9$ : $9(f + 1)$ .
Factor out common binomial: Factor out the common binomial $(f + 1)$ . We have $2f(f + 1) + 9(f + 1)$ . Factor out the common binomial $(f + 1)$ to get $(f + 1)(2f + 9)$ .