Factor 6x^2-11x-10

Problem

6*x2−11*x−10

Solution

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

2. Calculate the product a*c which is 6⋅(−10)=−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: −15*x+4*x

6*x2−15*x+4*x−10

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)+2*(2*x−5)

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

(3*x+2)*(2*x−5)

Final Answer

6*x2−11*x−10=(3*x+2)*(2*x−5)

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