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$f(x)=x^4-16x^2+4$, the root of $f(x)$ is $a= \sqrt{3} + \sqrt{5}$

Factorise $f(x)$ as a product of irreducible polynomials over $\mathbb{Q}$, over $\mathbb{R}$ and over $\mathbb{C}$.

I am really confused as to how to start.

  • 1
    use the quadratic formula, twice if neessary.2012-11-13
  • 5
    Please don't yell at us. It's rude.2012-11-13
  • 1
    How do you mean, "the root"? This polynomial has more than one root.2012-11-13

2 Answers 2