The value of the polynomial at given point. Given that:
$f(x)=x^{10}+2x^9-2x^8-2x^7+x^6+3x^2+6x+1$.
Find the value of $f(x)$ at $x=\sqrt{2}-1$
Answer is an integer. I tried factorization but couldn't proceed towards anything promising.

$$f(x)=x^{10}+2x^9-2x^8-2x^7+x^6+3x^2+6x+1\\=x(x((x-1)(x+1)(x(x+2)-1)x^4+3)+6)+1$$
$\Longrightarrow f(\sqrt 2 -1)=\boxed{\color{red}{4}}$
