Factor 2x^2-7x+5

Problem

2*x2−7*x+5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−7 and c=5

2. Find two numbers that multiply to a⋅c=10 and add to b=−7

3. Determine that the two numbers are −2 and −5 because (−2)*(−5)=10 and −2+(−5)=−7

4. Rewrite the middle term −7*x using these two numbers: 2*x2−2*x−5*x+5

5. Factor by grouping the first two terms and the last two terms: 2*x*(x−1)−5*(x−1)

6. Factor out the common binomial factor (x−1)

Final Answer

2*x2−7*x+5=(2*x−5)*(x−1)

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