Factor 3x^2-17x+10

Problem

3*x2−17*x+10

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−17 and c=10

2. Calculate the product of a and c which is 3⋅10=30

3. Find two numbers that multiply to 30 and add to the middle coefficient b=−17 These numbers are −15 and −2

4. Rewrite the middle term −17*x using the two numbers found: −15*x−2*x

3*x2−15*x−2*x+10

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)−2*(x−5)

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

(3*x−2)*(x−5)

Final Answer

3*x2−17*x+10=(3*x−2)*(x−5)

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