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Given that m - 2 is a positive integer that divides 3m^2 - 2m + 11, find the sum of all such values of m.

 Jan 11, 2020
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"Given that m - 2 is a positive integer that divides 3m^2 - 2m + 11, find the sum of all such values of m."

 

\(\frac{3m^2-2m+11}{m-2}=3m+4+\frac{19}{m-2}\)

 

For the last term to be an integer we must have m - 2 = 1, so m = 3;  or  m - 2 = 19, so m = 21

 

Hence sum = 3 + 21 = 24

 Jan 11, 2020

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