高次方程的奥数题
Show that no one \( n \)th root of a rational (for \( n \) a positive integer) can be a root of the polynomial \(x^5-x^4-4x^3+4x^2+2\).show that the polynomial \(x^4+3x^3+6x^2+9x+12\) cannot be written as the product of \( 2 \) polynomial of degree \( 2 \) with integer coefficients. 这么简单的排版，就不要用贴图了吧（我已用字符帮你排版了一遍，同时删除了不必要的图片）。
另请注意版规：既然标明“转载”——“请尊重知识产权：若非原创，请务必注明出处（若为链接，则必须是可直达的）！” 第二题很简单，用Eisenstein准则，取p=3，原多项式在有理数域上不可约
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