Factor. 6n^2 + 72n - 78 ____

Identify GCF of coefficients: Identify the greatest common factor (GCF) of the coefficients 6, 72, and -78. GCF = 6.Factor out GCF: Factor out the GCF from the quadratic expression. 6(n^2 + 12n - 13).Find two numbers: Look for two numbers that multiply to -13 * 6 = -78 and add up to 12. The numbers are 14 and -6.Rewrite middle term: Rewrite the middle term using the numbers found. 6(n^2 + 14n - 6n - 13).Factor by grouping: Factor by grouping. 6((n^2 + 14n) - (6n + 13)).Factor out common factor: Factor out the common factor from each group. 6(n(n + 14) - 1(n + 14)).Factor out common binomial factor: Factor out the common binomial factor (n + 14). 6(n - 1)(n + 14).

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Algebra 2

Factor quadratics

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Q. Factor.

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6n^2 + 72n - 78

Identify GCF of coefficients: Identify the greatest common factor (GCF) of the coefficients $6$ , $72$ , and $-78$ . $\text{GCF} = 6.$
Factor out GCF: Factor out the GCF from the quadratic expression. $6(n^2 + 12n - 13)$ .
Find two numbers: Look for two numbers that multiply to $-13 \times 6 = -78$ and add up to $12$ . The numbers are $14$ and $-6$ .
Rewrite middle term: Rewrite the middle term using the numbers found. $\newline$ $6(n^2 + 14n - 6n - 13)$ .
Factor by grouping: Factor by grouping. $6((n^2 + 14n) - (6n + 13))$ .
Factor out common factor: Factor out the common factor from each group. $6(n(n + 14) - 1(n + 14))$ .
Factor out common binomial factor: Factor out the common binomial factor $(n + 14)$ . $\newline$ $6(n - 1)(n + 14)$ .