Factor 5x^2-13x+6

Problem

5*x2−13*x+6

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=5 b=−13 and c=6

2. Calculate the product of a and c which is 5×6=30

3. Find two numbers that multiply to 30 and add to the middle coefficient b=−13 These numbers are −10 and −3

4. Rewrite the middle term −13*x using the two numbers found: 5*x2−10*x−3*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−2)−3*(x−2)

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

Final Answer

5*x2−13*x+6=(5*x−3)*(x−2)

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