Factor 2x^2-7x+6

Problem

2*x2−7*x+6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−7 and c=6

2. Find two numbers that multiply to a⋅c=12 and add to b=−7

3. Determine the pair of numbers, which are −3 and −4 since (−3)⋅(−4)=12 and (−3)+(−4)=−7

4. Rewrite the middle term −7*x using these two numbers: 2*x2−4*x−3*x+6

5. Factor by grouping the first two terms and the last two terms: 2*x*(x−2)−3*(x−2)

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

Final Answer

2*x2−7*x+6=(2*x−3)*(x−2)

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