Factor 2x^2-9x+7

Problem

2*x2−9*x+7

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−9 and c=7

2. Find two numbers that multiply to a*c=2⋅7=14 and add to b=−9

3. Determine the pair of numbers, which are −2 and −7 since (−2)*(−7)=14 and −2+(−7)=−9

4. Rewrite the middle term −9*x using the two numbers found: 2*x2−2*x−7*x+7

5. Factor by grouping the first two terms and the last two terms: 2*x*(x−1)−7*(x−1)

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

Final Answer

2*x2−9*x+7=(2*x−7)*(x−1)

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