Factor 2x^2-5x-7

Problem

2*x2−5*x−7

Solution

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

2. Calculate the product of a and c which is 2×−7=−14

3. Find two numbers that multiply to −14 and add to the middle coefficient b=−5 These numbers are −7 and 2

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

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 2*x*(x+1)−7*(x+1)

6. Factor out the common binomial (x+1) to obtain the final factored form.

Final Answer

2*x2−5*x−7=(2*x−7)*(x+1)

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