Factor 3x^2+2x-1

Problem

3*x2+2*x−1

Solution

1. Identify the coefficients a b and c from the quadratic expression a*x2+b*x+c where a=3 b=2 and c=−1

2. Find two numbers that multiply to a⋅c=3⋅(−1)=−3 and add to b=2

3. Determine the pair of numbers, which are 3 and −1 since 3⋅(−1)=−3 and 3 + (-1) = 2$.

4. Rewrite the middle term 2*x using the pair of numbers found: 3*x−x

3*x2+3*x−x−1

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

3*x*(x+1)−1*(x+1)

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

(3*x−1)*(x+1)

Final Answer

3*x2+2*x−1=(3*x−1)*(x+1)

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