Let
![n > 1](/media/m/c/8/9/c8999d29e042cf52e485c7a7b7301b0a.png)
be an integer and let
![f(x) = x^n + 5 \cdot x^{n-1} + 3.](/media/m/b/6/a/b6ae45b9b1081a69b93fa400805a6c0b.png)
Prove that there do not exist polynomials
![g(x),h(x),](/media/m/6/5/c/65cc6dc62e49afd16231a6907affdd20.png)
each having integer coefficients and degree at least one, such that
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Let $n > 1$ be an integer and let $f(x) = x^n + 5 \cdot x^{n-1} + 3.$ Prove that there do not exist polynomials $g(x),h(x),$ each having integer coefficients and degree at least one, such that $f(x) = g(x) \cdot h(x).$