Factor 12x^2-5x-3

Problem

12*x2−5*x−3

Solution

1. Identify the coefficients a b and c from the quadratic expression a*x2+b*x+c where a=12 b=−5 and c=−3

2. Calculate the product a*c which is 12×−3=−36

3. Find two numbers that multiply to −36 and add to the middle coefficient b=−5 These numbers are −9 and 4

4. Rewrite the middle term −5*x using the two numbers found: −9*x+4*x

12*x2−9*x+4*x−3

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

3*x*(4*x−3)+1*(4*x−3)

6. Factor out the common binomial (4*x−3)

(3*x+1)*(4*x−3)

Final Answer

12*x2−5*x−3=(3*x+1)*(4*x−3)

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