The Factor Square Property (FSP) is the divisibility of the polynomial $f(x^2)$ by $f(x)$.
Is $x^2+x+1$ the only FSP irreducible polynomial of degree $2$ ?
Are there other linear polynomial besides $x$ and $x-1$ with FSP?
Do we have other FSP irreducible polynomials of degree $3$ or $4$? Any of these have integer coefficients??
Are there any other observations you can make about polynomials with FSP?
But the solutions use cyclotomic polynomials. Is there an easier solution? The Question is from Ross MathCamp, so, I suppose they will give some observation based question which doesn't require any kind of Complex Numbers I suppose.