Factor 10x^2-13x-3

Problem

10*x2−13*x−3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=10 b=−13 and c=−3

2. Calculate the product of a and c which is 10⋅−3=−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: 10*x2−15*x+2*x−3

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 5*x*(2*x−3)+1*(2*x−3)

6. Factor out the common binomial (2*x−3) to obtain the final factored form.

Final Answer

10*x2−13*x−3=(5*x+1)*(2*x−3)

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