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 since 2⋅(−1)=−2 and 2 + (-1) = 1$.

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

2*x2+2*x−x−1

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)−1*(x+1)

6. Factor out the common binomial (x+1)

(2*x−1)*(x+1)

Final Answer

2*x2+x−1=(2*x−1)*(x+1)

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