Factor. v^2 + 20v + 19 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression v^2 + 20v + 19. Compare v^2 + 20v + 19 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 20, and c = 19.Compare with standard form: Find two numbers whose product is equal to ac (since a = 1, just c) and whose sum is equal to b. We need two numbers that multiply to 19 and add up to 20. The numbers 1 and 19 satisfy these conditions because: 1 * 19 = 19 and 1 + 19 = 20.Find product and sum: Write the quadratic expression using the two numbers found in Step 2 to split the middle term. v^2 + 20v + 19 can be rewritten as: v^2 + 1v + 19v + 19Write using two numbers: Factor by grouping. Group the terms to factor out the common factors: (v^2 + 1v) + (19v + 19) Factor out a v from the first group and 19 from the second group: v(v + 1) + 19(v + 1)Factor by grouping: Factor out the common binomial factor. Both groups contain the factor (v + 1), so factor this out: (v + 1)(v + 19)

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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v^2 + 20v + 19

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $v^2 + 20v + 19$ . Compare $v^2 + 20v + 19$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Compare with standard form: Find two numbers whose product is equal to $ac$ (since $a = 1$ , just $c$ ) and whose sum is equal to $b$ . We need two numbers that multiply to $19$ and add up to $20$ . The numbers $1$ and $19$ satisfy these conditions because: $1 \times 19 = 19$ and $1 + 19 = 20$ .
Find product and sum: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $\newline$ $v^2 + 20v + 19$ can be rewritten as: $\newline$ $v^2 + 1v + 19v + 19$
Write using two numbers: Factor by grouping. $\newline$ Group the terms to factor out the common factors: $\newline$ $v^2 + 1v$ + $19v + 19$ $\newline$ Factor out a $v$ from the first group and $19$ from the second group: $\newline$ $v(v + 1) + 19(v + 1)$
Factor by grouping: Factor out the common binomial factor. $\newline$ Both groups contain the factor $(v + 1)$ , so factor this out: $\newline$ $(v + 1)(v + 19)$