Factor 2x^2-11x+5

Problem

2*x2−11*x+5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−11 and c=5

2. Find two numbers that multiply to a⋅c=10 and add to b=−11 These numbers are −10 and −1

3. Rewrite the middle term −11*x using the two numbers found: −10*x and −1*x

2*x2−10*x−x+5

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

2*x*(x−5)−1*(x−5)

5. Factor out the common binomial (x−5)

(2*x−1)*(x−5)

Final Answer

2*x2−11*x+5=(2*x−1)*(x−5)

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