Let $f(x) = x^4 − x^3 + 2x^2 − 3x − 3$
Show that f(x) is reducible over $\Bbb{Q}$
Rational zeros shows there is no roots i tried writing $(x^2+bx+c)(x^2+dx+e)$ and then tried to solve the equations for each of letters but it got crazy ugly which lead me to the conclusion there must be a better way...
Answer
i think that is a good idea, it is $$(x^2+3)(x^2-x-1)=f(x)$$
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