Factor 15n^2-27n-6

Problem

15*n2−27*n−6

Solution

1. Factor out the greatest common factor (GCF) from all three terms, which is 3

3*(5*n2−9*n−2)

2. Identify the coefficients of the quadratic expression inside the parentheses, a*x2+b*x+c where a=5 b=−9 and c=−2

3. Find two numbers that multiply to a⋅c=5⋅(−2)=−10 and add to b=−9 These numbers are −10 and 1

4. Rewrite the middle term −9*n using the two numbers found in the previous step.

3*(5*n2−10*n+n−2)

5. Factor by grouping the terms inside the parentheses.

3*((5*n2−10*n)+(n−2))

6. Extract the common factors from each group.

3*(5*n*(n−2)+1*(n−2))

7. Factor out the common binomial (n−2)

3*(5*n+1)*(n−2)

Final Answer

15*n2−27*n−6=3*(5*n+1)*(n−2)

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