Question 118
Let $n \gt 2$ be an integer and
$$
f(x) = x^n + x^{n-1} - x^{n-2} - 3.
$$
Prove that $f(x)$ cannot be factored as the product of two polynomials with integer coefficients and degree less than $n$.
$$
f(x) = x^n + x^{n-1} - x^{n-2} - 3.
$$
Prove that $f(x)$ cannot be factored as the product of two polynomials with integer coefficients and degree less than $n$.