Factor 6x^2-19x+10

Problem

6*x2−19*x+10

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=−19 and c=10

2. Calculate the product a*c by multiplying 6×10=60

3. Find two numbers that multiply to 60 and add to −19 These numbers are −15 and −4

4. Rewrite the middle term −19*x using the two numbers found: 6*x2−15*x−4*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*(2*x−5)−2*(2*x−5)

6. Factor out the common binomial (2*x−5) to obtain the final factored form.

Final Answer

6*x2−19*x+10=(3*x−2)*(2*x−5)

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