Factoring a hard polynomial This might seem like a basic question but I want a systematic way to factor the following polynomial:
$$n^4+6n^3+11n^2+6n+1.$$
I know the answer but I am having a difficult time factoring this polynomial properly. (It should be $(n^2 + 3n + 1)^2$). Thank you and have a great day!

I was thinking along the same lines as TZakrevskiy but with a slight twist.  Once you've become convinced that $P(n)=n^4+6n^3+11n^2+6n+1$ is the square of a quadratic (because its values for small $n$ are all squares), try computing
$$P(10)=10000+6000+1100+60+1=17161$$
and then take its square root:
$$\sqrt{17161}=131=1\cdot10^2+3\cdot10+1$$
which suggests the (correct) factorization
$$P(n)=(n^2+3n+1)^2$$
If you want to be extra sure, look at
$$\sqrt{100^4+6\cdot100^3+11\cdot100^2+6\cdot100+1}=10301$$
