Factor. 9k^2 - 18k - 27 ____

Identify coefficients: Identify the coefficients of the quadratic expression: a = 9, b = -18, c = -27.Find suitable numbers: Look for two numbers that multiply to a*c (9*-27 = -243) and add up to b (-18).Apply numbers to expression: The numbers that work are -27 and +9 because -27 * 9 = -243 and -27 + 9 = -18.Rewrite middle term: Rewrite the middle term using the numbers found: 9k^2 - 27k + 9k - 27.Group the terms: Group the terms: (9k^2 - 27k) + (9k - 27).Factor out common factors: Factor out the common factors from each group: 9k(k - 3) + 9(k - 3).Factor out common binomial: Factor out the common binomial: (k - 3)(9k + 9).Factor out common factor: Factor out the common factor of 9 from the second binomial: (k - 3)(9)(k + 1).Write final factored form: Write the final factored form: 9(k - 3)(k + 1).

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Math Problems

Algebra 2

Factor quadratics

Full solution

Q. Factor.

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9k^2 - 18k - 27

Identify coefficients: Identify the coefficients of the quadratic expression: $a = 9$ , $b = -18$ , $c = -27$ .
Find suitable numbers: Look for two numbers that multiply to $a*c$ ( $9*-27 = -243$ ) and add up to $b$ ( $-18$ ).
Apply numbers to expression: The numbers that work are $-27$ and $+9$ because $-27 \times 9 = -243$ and $-27 + 9 = -18$ .
Rewrite middle term: Rewrite the middle term using the numbers found: $9k^2 - 27k + 9k - 27$ .
Group the terms: Group the terms: $9k^2 - 27k$ + $9k - 27$ .
Factor out common factors: Factor out the common factors from each group: $9k(k - 3) + 9(k - 3)$ .
Factor out common binomial: Factor out the common binomial: $(k - 3)(9k + 9)$ .
Factor out common factor: Factor out the common factor of $9$ from the second binomial: $(k - 3)(9)(k + 1)$ .
Write final factored form: Write the final factored form: $9(k - 3)(k + 1)$ .