\[\begin{array}{l}
c)\,\,\forall n \in N,\,\,3{n^2} + 15n + 12\,\,\, \vdots \,\,6\\
A = 3{n^2} + 15n + 12 = 3\left( {{n^2} + 5n + 4} \right)\\
= 3\left( {n + 1} \right)\left( {n + 4} \right)\\
Ta\,\,co:\,\,\,A\,\, \vdots \,\,3\,\,\forall n\\
De\,\,CM\,\,\,A\,\, \vdots \,\,6\,\,\,ta\,\,\,can\,\,\,CM\,\,\,A\,\, \vdots \,\,2\\
Ta\,\,co:\,\,\,\left( {n + 1} \right)\,\,\,va\,\,\left( {n + 4} \right)\,\,\,la\,\,\,1\,\,\,so\,\,le\,\,\,va\,\,\,1\,\,\,so\,\,chan\,\,\,voi\,\,\,\forall n\\
\Rightarrow \left( {n + 1} \right)\left( {n + 4} \right)\,\,\,la\,\,\,1\,\,\,so\,\,chan.\\
\Rightarrow \left( {n + 1} \right)\left( {n + 4} \right)\,\, \vdots \,\,2\,\,\,\forall n\\
\Rightarrow A = 3\left( {n + 1} \right)\left( {n + 4} \right)\,\,\, \vdots \,\,\,6\,\,\,\forall n.\\
b)\,\,\,\forall n \in N:\,\,{n^3} + n + 1\,\,\, \vdots \,\,\,3\\
Cau\,\,nay\,\,\,e\,\,gui\,\,\,de\,\,day\,\,du\,\,nhe,
\end{array}\]
