Question 1024869
The description for #1 is wrong.  Review the Remainder Theorem.  A nonzero remainder means that the factor is not one of the root factors for the function.


You can perform the polynomial division for {{{(x^3+mx^2+nx+6)/(x-1)}}}, very difficult to try to show here.  The expression for the remainder will be {{{m+n+7}}}.  The quotient without the remainder will be  {{{x^2+(m+1)x+(m+n+1)}}}.


Maybe this is enough to be helpful for you.