## One root of the polynomial f(x) = 5$x^2$ + $x^4$-5$x^3$-$x^2$-10x-2 over $\mathbb C$ is $i$. November 30

One root of the polynomial f(x) = 5$x^2$ + $x^4$-5$x^3$-$x^2$-10x-2 over $\mathbb C$ is $i$.(a) Write $f(x)$ as a product of irreducible polynomials in $\mathbb Q[x]$.(b) Write $f(x)$ as a product of irreducible polynomials in $\mathbb R[x]$.(c) Writ