Factor 6x^2-19x+15

Problem

6*x2−19*x+15

Solution

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

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

a*c=6⋅15=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.

6*x2−9*x−10*x+15

5. Factor by grouping the first two terms and the last two terms.

3*x*(2*x−3)−5*(2*x−3)

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

(3*x−5)*(2*x−3)

Final Answer

6*x2−19*x+15=(3*x−5)*(2*x−3)

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