Factor. 9z^2 + 72z - 81 ____

Identify coefficients: Identify the coefficients of the quadratic expression: a = 9, b = 72, c = -81.Find suitable numbers: Look for two numbers that multiply to a*c (9*-81 = -729) and add to b (72).Use numbers found: The numbers that work are 81 and -9 because 81*-9 = -729 and 81-9 = 72.Rewrite middle term: Rewrite the middle term using the two numbers found: 9z^2 + 81z - 9z - 81.Factor by grouping: Factor by grouping: (9z^2 + 81z) - (9z + 81).Factor out common factors: Factor out the common factors from each group: 9z(z + 9) - 9(z + 9).Factor out common binomial: Factor out the common binomial (z + 9): 9(z + 9)(z - 9).

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Algebra 2

Factor quadratics

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Q. Factor.

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9z^2 + 72z - 81

Identify coefficients: Identify the coefficients of the quadratic expression: $a = 9$ , $b = 72$ , $c = -81$ .
Find suitable numbers: Look for two numbers that multiply to $a*c$ ( $9*-81 = -729$ ) and add to $b$ ( $72$ ).
Use numbers found: The numbers that work are $81$ and $-9$ because $81 \times -9 = -729$ and $81-9 = 72$ .
Rewrite middle term: Rewrite the middle term using the two numbers found: $9z^2 + 81z - 9z - 81$ .
Factor by grouping: Factor by grouping: $(9z^2 + 81z) - (9z + 81)$ .
Factor out common factors: Factor out the common factors from each group: $9z(z + 9) - 9(z + 9)$ .
Factor out common binomial: Factor out the common binomial $(z + 9)$ : $9(z + 9)(z - 9)$ .