Factor 2x^2-x-1

Problem

2*x2−x−1

Solution

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

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

3. Determine the pair of numbers, which are −2 and 1

4. Rewrite the middle term −x using these two numbers as −2*x+x

5. Group the terms into two pairs: (2*x2−2*x)+(x−1)

6. Factor out the greatest common factor from each group: 2*x*(x−1)+1*(x−1)

7. Factor out the common binomial (x−1) to obtain the final factored form.

Final Answer

2*x2−x−1=(2*x+1)*(x−1)

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