#1**+1 **

Assuming that m is an integer, we must have \(\frac {3m^2-2m+11} {m-2}=N\), where N is an integer. So since

\(N=\frac{3m^2-2m+11} {m-2}=3m+4+\frac{19} {m-2}\), the fraction\(\frac{19} {m-2}\)must be an integer. But since the numerator of this fraction is prime, its only divisors are \(\pm 1\) and \(\pm19\). So we must have \(m-2=\pm1\) and \(m-2=\pm19\). By solving these equations for m you get four possible values for m. Have fun!

Gadfly Nov 11, 2019