Factor 2x^2-11x-21

Problem

2*x2−11*x−21

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=−11 and c=−21

2. Calculate the product of a and c which is 2×−21=−42

3. Find two numbers that multiply to −42 and add to the middle coefficient b=−11 These numbers are −14 and 3

4. Rewrite the middle term −11*x using the two numbers found: 2*x2−14*x+3*x−21

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 2*x*(x−7)+3*(x−7)

6. Factor out the common binomial (x−7) to obtain the final factored form.

Final Answer

2*x2−11*x−21=(2*x+3)*(x−7)

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