Factor. u^2 + 20u + 19 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression u^2 + 20u + 19. Compare u^2 + 20u + 19 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 20, and c = 19.Find product and sum: 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.Split middle term: Write the quadratic expression using the two numbers found in Step 2 to split the middle term. u^2 + 20u + 19 can be rewritten as: u^2 + 1u + 19u + 19.Factor by grouping: Factor by grouping. Group the terms to factor out common factors: (u^2 + 1u) + (19u + 19). Factor out a u from the first group and 19 from the second group: u(u + 1) + 19(u + 1).Factor common binomial: Factor out the common binomial factor. Both groups contain the common factor (u + 1), so factor this out: (u + 1)(u + 19).

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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u^2 + 20u + 19

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $u^2 + 20u + 19$ . Compare $u^2 + 20u + 19$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Find product and sum: 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 $1 + 19 = 20$ .
Split middle term: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $\newline$ $u^2 + 20u + 19$ can be rewritten as: $\newline$ $u^2 + 1u + 19u + 19$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms to factor out common factors: $\newline$ $(u^2 + 1u) + (19u + 19)$ . $\newline$ Factor out a $u$ from the first group and $19$ from the second group: $\newline$ $u(u + 1) + 19(u + 1)$ .
Factor common binomial: Factor out the common binomial factor. $\newline$ Both groups contain the common factor $(u + 1)$ , so factor this out: $\newline$ $(u + 1)(u + 19)$ .