MathDB
Q 7

Source:

May 25, 2007
algebrapolynomialcalculusintegrationnumber theoryrelatively primeRational Root Theorem

Problem Statement

Let f(x)=xn+5xnāˆ’1+3f(x)=x^{n}+5x^{n-1}+3, where n>1n>1 is an integer. Prove that f(x)f(x) cannot be expressed as the product of two nonconstant polynomials with integer coefficients.