Factor 2x^2-x-21

Problem

2*x2−x−21

Solution

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

2. Find two numbers that multiply to a⋅c=2⋅(−21)=−42 and add to b=−1

3. Determine the pair of numbers, which are −7 and 6 since (−7)⋅6=−42 and −7+6=−1

4. Rewrite the middle term −x using these two numbers as −7*x+6*x

2*x2−7*x+6*x−21

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

x*(2*x−7)+3*(2*x−7)

6. Factor out the common binomial (2*x−7)

(x+3)*(2*x−7)

Final Answer

2*x2−x−21=(2*x−7)*(x+3)

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