Factor 3x^2-2x-1

Problem

3*x2−2*x−1

Solution

1. Identify the coefficients of 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 two numbers found: 3*x2−3*x+x−1

5. Factor by grouping the terms into two pairs: (3*x2−3*x)+(x−1)

6. Factor out the greatest common factor from each pair: 3*x*(x−1)+1*(x−1)

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

Final Answer

3*x2−2*x−1=(3*x+1)*(x−1)

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