With which natural value of n, the polynomial will be prime value and why? So. $P(n) = n^4 + n^2 + 1$ is a polynomial. I calculated that answer is 1.
But I don't understand why?

We have
$$n^4+n^2=(n^2-n+1)(n^2+n+1).\tag{1}$$
If $n\gt 1$, each term on the right-hand side of (1) is greater than $1$, so $n^4+n^2+1$ cannot be prime.
Remark: One way of "seeing" the above factorization is to note that
$$n^4+n^2+1=(n^2+1)^2-n^2.$$
Now we can use the usual factorization of a difference of squares.
