Factor 5x^2-13x-6

Problem

5*x2−13*x−6

Solution

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

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

5*x2−15*x+2*x−6

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

5*x*(x−3)+2*(x−3)

6. Factor out the common binomial (x−3)

(5*x+2)*(x−3)

Final Answer

5*x2−13*x−6=(5*x+2)*(x−3)

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