Factor 5x^2-17x+6

Problem

5*x2−17*x+6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=−17 and c=6

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

5⋅6=30

3. Find two numbers that multiply to 30 and add to the middle coefficient b=−17

−15⋅−2=30

−15+(−2)=−17

4. Rewrite the middle term −17*x using the two numbers found in the previous step.

5*x2−15*x−2*x+6

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

5*x*(x−3)−2*(x−3)

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

(5*x−2)*(x−3)

Final Answer

5*x2−17*x+6=(5*x−2)*(x−3)

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