Identify Variables: Step 1: Identify a, b, and c in the quadratic expression z^2 + 9z + 20. Here, a = 1, b = 9, and c = 20.Find Number Pairs: Step 2: Find two numbers that multiply to ac (1*20 = 20) and add up to b (9). Possible pairs: (1, 20), (2, 10), (4, 5). Correct pair: (4, 5) because 4 + 5 = 9.Factor the Quadratic: Step 3: Use the numbers from Step 2 to factor the quadratic. z^2 + 9z + 20 = z^2 + 4z + 5z + 20 Group the terms: (z^2 + 4z) + (5z + 20) Factor out the common terms: z(z + 4) + 5(z + 4) Factor by grouping: (z + 5)(z + 4)

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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z^{2}+9 z+20

Identify Variables: Step $1$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $z^2 + 9z + 20$ . Here, $a = 1$ , $b = 9$ , and $c = 20$ .
Find Number Pairs: Step $2$ : Find two numbers that multiply to $ac$ ( $1\times20 = 20$ ) and add up to $b$ ( $9$ ). $\newline$ Possible pairs: $(1, 20)$ , $(2, 10)$ , $(4, 5)$ . $\newline$ Correct pair: $(4, 5)$ because $4 + 5 = 9$ .
Factor the Quadratic: Step $3$ : Use the numbers from Step $2$ to factor the quadratic. $\newline$ $z^2 + 9z + 20 = z^2 + 4z + 5z + 20$ $\newline$ Group the terms: $(z^2 + 4z) + (5z + 20)$ $\newline$ Factor out the common terms: $z(z + 4) + 5(z + 4)$ $\newline$ Factor by grouping: $(z + 5)(z + 4)$