Factor. 2v^2 + 9v + 9 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 2v^2 + 9v + 9. Compare 2v^2 + 9v + 9 with 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). We need to find two numbers that multiply to 18 and add up to 9. The numbers 6 and 3 satisfy these conditions because 6*3 = 18 and 6+3 = 9.Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step 2. 2v^2 + 9v + 9 can be rewritten as 2v^2 + 6v + 3v + 9.Factor by grouping: Factor by grouping. Group the terms: (2v^2 + 6v) + (3v + 9). Factor out the common factor from each group. From the first group, factor out 2v: 2v(v + 3). From the second group, factor out 3: 3(v + 3).Factor out common binomial: Factor out the common binomial. We have 2v(v + 3) + 3(v + 3). The common binomial is (v + 3). Factor out (v + 3) to get (v + 3)(2v + 3).

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Factor. $\newline$ $2v^2 + 9v + 9$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2v^2 + 9v + 9

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2v^2 + 9v + 9$ . Compare $2v^2 + 9v + 9$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*9 = 18$ ) and add up to $b$ ( $9$ ). $\newline$ We need to find two numbers that multiply to $18$ and add up to $9$ . $\newline$ The numbers $6$ and $3$ satisfy these conditions because $6*3 = 18$ and $6+3 = 9$ .
Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step $2$ . $\newline$ $2v^2 + 9v + 9$ can be rewritten as $2v^2 + 6v + 3v + 9$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $2v^2 + 6v$ + $3v + 9$ . $\newline$ Factor out the common factor from each group. $\newline$ From the first group, factor out $2v$ : $2v(v + 3)$ . $\newline$ From the second group, factor out $3$ : $3(v + 3)$ .
Factor out common binomial: Factor out the common binomial. $\newline$ We have $2v(v + 3) + 3(v + 3)$ . $\newline$ The common binomial is $(v + 3)$ . $\newline$ Factor out $(v + 3)$ to get $(v + 3)(2v + 3)$ .