Factor 6x^2-13x-5

Problem

6*x2−13*x−5

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=6 b=−13 and c=−5

2. Calculate the product of a and c which is 6×−5=−30

3. Find two numbers that multiply to −30 and add to the middle coefficient b=−13 These numbers are −15 and 2

4. Rewrite the middle term −13*x using the two numbers found: 6*x2−15*x+2*x−5

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

3*x*(2*x−5)+1*(2*x−5)

6. Factor out the common binomial (2*x−5)

(3*x+1)*(2*x−5)

Final Answer

6*x2−13*x−5=(3*x+1)*(2*x−5)

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