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Factor.\newline6n2+72n−786n^2 + 72n - 78

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Full solution

Q. Factor.\newline6n2+72n−786n^2 + 72n - 78
  1. Identify GCF of coefficients: Identify the greatest common factor (GCF) of the coefficients 66, 7272, and −78-78.GCF=6.\text{GCF} = 6.
  2. Factor out GCF: Factor out the GCF from the quadratic expression. 6(n2+12n−13)6(n^2 + 12n - 13).
  3. Find two numbers: Look for two numbers that multiply to −13×6=−78-13 \times 6 = -78 and add up to 1212. The numbers are 1414 and −6-6.
  4. Rewrite middle term: Rewrite the middle term using the numbers found.\newline6(n2+14n−6n−13)6(n^2 + 14n - 6n - 13).
  5. Factor by grouping: Factor by grouping. 6((n2+14n)−(6n+13))6((n^2 + 14n) - (6n + 13)).
  6. Factor out common factor: Factor out the common factor from each group. 6(n(n+14)−1(n+14))6(n(n + 14) - 1(n + 14)).
  7. Factor out common binomial factor: Factor out the common binomial factor (n+14)(n + 14).\newline6(n−1)(n+14)6(n - 1)(n + 14).

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