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

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2f^2 + 9f + 9 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 9, c = 9Find two numbers: Find two numbers that multiply to a*c (2*9 = 18) and add up to b (9). The numbers that satisfy these conditions are 3 and 6, since 3*6 = 18 and 3+6 = 9.Rewrite middle term: Rewrite the middle term 9f using the two numbers found in the previous step. 2f^2 + 9f + 9 can be rewritten as 2f^2 + 3f + 6f + 9.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. (2f^2 + 3f) + (6f + 9)Factor out common factor: Factor out the greatest common factor from each group. f(2f + 3) + 3(2f + 3)Final factored form: Since both groups contain the common factor (2f + 3), factor this out. (f + 3)(2f + 3) is the factored form of the quadratic expression.

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2f^2 + 9f + 9

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2f^2 + 9f + 9$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 9$ , $c = 9$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*9 = 18$ ) and add up to $b$ ( $9$ ). $\newline$ The numbers that satisfy these conditions are $3$ and $6$ , since $3*6 = 18$ and $3+6 = 9$ .
Rewrite middle term: Rewrite the middle term $9f$ using the two numbers found in the previous step. $\newline$ $2f^2 + 9f + 9$ can be rewritten as $2f^2 + 3f + 6f + 9$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(2f^2 + 3f) + (6f + 9)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $f(2f + 3) + 3(2f + 3)$
Final factored form: Since both groups contain the common factor $(2f + 3)$ , factor this out. $(f + 3)(2f + 3)$ is the factored form of the quadratic expression.