Factor 15x^2-19x+6

Problem

15*x2−19*x+6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=15 b=−19 and c=6

2. Calculate the product a*c by multiplying 15 and 6

a*c=15⋅6=90

3. Find two numbers that multiply to 90 and add to the middle coefficient b=−19

−9⋅−10=90

−9+(−10)=−19

4. Rewrite the middle term −19*x using the two numbers found.

15*x2−9*x−10*x+6

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

3*x*(5*x−3)−2*(5*x−3)

6. Factor out the common binomial (5*x−3)

(3*x−2)*(5*x−3)

Final Answer

15*x2−19*x+6=(3*x−2)*(5*x−3)

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