Factor 10x^2-11x-6

Problem

10*x2−11*x−6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=10 b=−11 and c=−6

2. Calculate the product a*c by multiplying 10 and −6 which gives a*c=−60

3. Find two numbers that multiply to −60 and add to the middle coefficient b=−11 These numbers are −15 and 4

4. Rewrite the middle term −11*x using the two numbers found: 10*x2−15*x+4*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*(2*x−3)+2*(2*x−3)

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

Final Answer

10*x2−11*x−6=(5*x+2)*(2*x−3)

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