Factor 12x^2+5x-2

Problem

12*x2+5*x−2

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=12 b=5 and c=−2

2. Calculate the product of a and c which is 12⋅−2=−24

3. Find two numbers that multiply to −24 and add to the middle coefficient b=5 These numbers are 8 and −3

4. Rewrite the middle term 5*x using the two numbers found: 8*x−3*x

12*x2+8*x−3*x−2

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

4*x*(3*x+2)−1*(3*x+2)

6. Factor out the common binomial factor (3*x+2)

(3*x+2)*(4*x−1)

Final Answer

12*x2+5*x−2=(3*x+2)*(4*x−1)

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