Factor 2x^2-13x+20

Problem

2*x2−13*x+20

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−13 and c=20

2. Calculate the product a*c which is 2×20=40

3. Find two numbers that multiply to 40 and add to the middle coefficient b=−13 These numbers are −8 and −5

4. Rewrite the middle term −13*x using the two numbers found: −8*x−5*x

2*x2−8*x−5*x+20

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

2*x*(x−4)−5*(x−4)

6. Factor out the common binomial (x−4)

(2*x−5)*(x−4)

Final Answer

2*x2−13*x+20=(2*x−5)*(x−4)

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