Factor. 2v^2 + 9v + 7 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2v^2 + 9v + 7 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 9, c = 7Find two numbers: Find two numbers that multiply to a*c (2*7 = 14) and add up to b (9). The numbers that satisfy these conditions are 2 and 7 because 2*7 = 14 and 2+7 = 9.Rewrite middle term: Rewrite the middle term 9v using the two numbers found in the previous step. 2v^2 + 9v + 7 can be rewritten as 2v^2 + 2v + 7v + 7.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. (2v^2 + 2v) + (7v + 7)Factor out common factor: Factor out the greatest common factor from each group. 2v(v + 1) + 7(v + 1)Final factorization: Since both groups contain the common factor (v + 1), factor this out. (2v + 7)(v + 1)

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Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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2v^2 + 9v + 7

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2v^2 + 9v + 7$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 9$ , $c = 7$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*7 = 14$ ) and add up to $b$ ( $9$ ). $\newline$ The numbers that satisfy these conditions are $2$ and $7$ because $2*7 = 14$ and $2+7 = 9$ .
Rewrite middle term: Rewrite the middle term $9v$ using the two numbers found in the previous step. $2v^2 + 9v + 7$ can be rewritten as $2v^2 + 2v + 7v + 7$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(2v^2 + 2v) + (7v + 7)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $2v(v + 1) + 7(v + 1)$
Final factorization: Since both groups contain the common factor $(v + 1)$ , factor this out. $(2v + 7)(v + 1)$