Factor 6x^2+13x-5

Problem

6*x2+13*x−5

Solution

1. Identify the coefficients of the quadratic expression 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: 15*x−2*x

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 factor (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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