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# help

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Given that m - 2 divides 3m^2 - 2m + 11, find all possible values of m.

Nov 11, 2019

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!