Factor. h^2 + 20h + 19 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression h^2 + 20h + 19. Compare h^2 + 20h + 19 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 20, and c = 19.Find numbers for ac: Find two numbers that multiply to ac (which is a * c) and add up to b. Since a = 1, we are looking for 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.Rewrite quadratic expression: Write the quadratic expression using the two numbers found in Step 2 to split the middle term. h^2 + 20h + 19 can be rewritten as h^2 + h + 19h + 19.Factor by grouping: Factor by grouping. Group the terms to factor out the common factors: (h^2 + h) + (19h + 19) Factor out an h from the first group and 19 from the second group: h(h + 1) + 19(h + 1)Factor out common binomial: Factor out the common binomial factor. Both groups contain the common factor (h + 1), so factor this out: (h + 1)(h + 19)

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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h^2 + 20h + 19

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