Factor 3x^2-19x+20

Problem

3*x2−19*x+20

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−19 and c=20

2. Multiply the leading coefficient a and the constant term c to find the product a*c

3⋅20=60

3. Find two numbers that multiply to 60 and add to the middle coefficient b=−19

−15⋅−4=60

−15+(−4)=−19

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

3*x2−15*x−4*x+20

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

3*x*(x−5)−4*(x−5)

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

(3*x−4)*(x−5)

Final Answer

3*x2−19*x+20=(3*x−4)*(x−5)

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