A bit of Galois Theory

Let $\mathbb Q[x]$ denote the set of polynomials with coefficients in $\mathbb Q$ .

Say $p(x) = \sum_{k=0}^{k=n} \lambda_k x^k$ , $\lambda_n \neq 0$ . We say the degree of $p(x)$ , denoted by $deg(p)$ , is $n$ .

We commonly say that a polynomial $p(x)$ is irreducible in $\mathbb Q[x]$ , if :

$(1) \qquad p \neq 0$

$(2) \qquad deg(p) >0$

$(3) \qquad if \ \exists q,h \in \mathbb Q[x] \ such \ that \ p(x)=q(x)h(x), then \ either$

$\ deg(q) \ or \ deg(h) \ is \ zero$ (that is, $\ one \ of \ \ h \ and \ g \ is \ a \ constant$ )

Now, consider : $x^4-2 \in \mathbb Q[x]$ . Is this polynomial irreducible in $\mathbb Q[x]$ ? If you think it is, let $a = -1$ , else, let $a =1$ . Same question for $x^4+4$ . If you think it is irreducible, take $b=0$ , else $b=3$ .

What is $a+b$ ?