Factor 6x^2-x-15

Problem

6*x2−x−15

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=6 b=−1 and c=−15

2. Calculate the product of a and c which is 6⋅(−15)=−90

3. Find two numbers that multiply to −90 and add to the middle coefficient b=−1 These numbers are −10 and 9

4. Rewrite the middle term −x using the two numbers found: −10*x+9*x

6*x2−10*x+9*x−15

5. Factor by grouping by splitting the expression into two pairs: (6*x2−10*x)+(9*x−15)

6. Factor out the greatest common factor from each pair.

2*x*(3*x−5)+3*(3*x−5)

7. Factor out the common binomial factor (3*x−5)

(2*x+3)*(3*x−5)

Final Answer

6*x2−x−15=(2*x+3)*(3*x−5)

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