Factor 3x^2-2x-8

Problem

3*x2−2*x−8

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=−8

2. Calculate the product a*c which is 3×−8=−24

3. Find two numbers that multiply to −24 and add to the middle coefficient b=−2 These numbers are −6 and 4

4. Rewrite the middle term −2*x using the two numbers found: 3*x2−6*x+4*x−8

5. Factor by grouping the first two terms and the last two terms: 3*x*(x−2)+4*(x−2)

6. Factor out the common binomial factor (x−2)

Final Answer

3*x2−2*x−8=(3*x+4)*(x−2)

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