`3n^2+5` chia hết cho `n-1`
⇔$\dfrac{3n^2+5}{n-1}$ `∈Z`
⇔$\dfrac{3(n^2-1)+8}{n-1}$ `∈Z`
⇔$\dfrac{3(n-1)(n+1)+8}{n-1}$ `∈Z`
⇔`3(n+1)+`$\dfrac{8}{n-1}$ `∈Z`
⇒`8` chia hết cho `n-1`
Mà `n-1∈Z`
⇒`n-1∈Ư(8)=``{±1,±2,±4,±8}`
⇒`n∈``{2, 0, 3, -1, 5, -3, 9, -7}`