Factor. v^2 + 18v - 19 ____

Find Numbers: First, we need to find two numbers that multiply to -19 and add up to 18.List Factors: Let's list the factors of -19: -1 and 19, 1 and -19.Identify Multiplication: Now, we see that 19 and -1 multiply to -19 and add up to 18.Write Middle Term: So, we can write the middle term 18v as 19v - v.Rewrite Expression: Now, rewrite the expression with the new middle terms: v^2 + 19v - v - 19.Factor by Grouping: Next, we factor by grouping. Group the first two terms and the last two terms: (v^2 + 19v) - (v + 19).Factor Common Factor: Factor out the common factor from each group: v(v + 19) - 1(v + 19).Factor Out Common Factor: Now, we see that (v + 19) is a common factor, so we factor it out: (v + 19)(v - 1).Check Solution: Check the solution by expanding: (v + 19)(v - 1) = v^2 - v + 19v - 19 = v^2 + 18v - 19.

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Algebra 2

Factor quadratics

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Q. Factor.

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v^2 + 18v - 19

Find Numbers: First, we need to find two numbers that multiply to $-19$ and add up to $18$ .
List Factors: Let's list the factors of $-19$ : $-1$ and $19$ , $1$ and $-19$ .
Identify Multiplication: Now, we see that $19$ and $-1$ multiply to $-19$ and add up to $18$ .
Write Middle Term: So, we can write the middle term $18v$ as $19v - v$ .
Rewrite Expression: Now, rewrite the expression with the new middle terms: $v^2 + 19v - v - 19$ .
Factor by Grouping: Next, we factor by grouping. Group the first two terms and the last two terms: $(v^2 + 19v) - (v + 19)$ .
Factor Common Factor: Factor out the common factor from each group: $v(v + 19) - 1(v + 19)$ .
Factor Out Common Factor: Now, we see that $(v + 19)$ is a common factor, so we factor it out: $(v + 19)(v - 1)$ .
Check Solution: Check the solution by expanding: v + \(19)(v - $1$ ) = v^ $2$ - v + $19$ v - $19$ = v^ $2$ + $18$ v - $19$ .\