Factor 10x^2-17x+3

Problem

10*x2−17*x+3

Solution

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

2. Calculate the product a*c by multiplying 10 and 3 which equals 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: 10*x2−15*x−2*x+3

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

5*x*(2*x−3)−1*(2*x−3)

6. Factor out the common binomial (2*x−3) to obtain the final factored form.

Final Answer

10*x2−17*x+3=(5*x−1)*(2*x−3)

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