Factor 2x^2-7x+3

Problem

2*x2−7*x+3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−7 and c=3

2. Find two numbers that multiply to a⋅c=6 and add to b=−7

3. Determine the pair of numbers, which are −6 and −1 since (−6)⋅(−1)=6 and (−6)+(−1)=−7

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

5. Factor by grouping the first two terms and the last two terms: 2*x*(x−3)−1*(x−3)

6. Factor out the common binomial (x−3) to obtain the final factored form.

Final Answer

2*x2−7*x+3=(2*x−1)*(x−3)

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