Factor 3x^2-x-2

Problem

3*x2−x−2

Solution

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

2. Find two numbers that multiply to a⋅c=3⋅(−2)=−6 and add to b=−1

3. Determine the two numbers, which are −3 and 2 since (−3)⋅2=−6 and −3+2=−1

4. Rewrite the middle term −x using these two numbers as −3*x+2*x

5. Group the terms into two pairs: (3*x2−3*x)+(2*x−2)

6. Factor out the greatest common factor from each pair: 3*x*(x−1)+2*(x−1)

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

Final Answer

3*x2−x−2=(3*x+2)*(x−1)

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