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: 14*x−3*x

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)

(2*x−3)*(x+7)

Final Answer

2*x2+11*x−21=(2*x−3)*(x+7)

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