consider a polynomial with integer coefficients in which the leading corfficient is not equal to 1. Can the related polynomial equation have a rational root that is an integer?

Question

Algebra 2: Consider a polynomial with integer coefficients in which the leading corfficient is not equal to 1. Can the related polynomial equation have a rational root that is an integer?

Answer 1

Yes. For example, 2x^3+2x^2-5x-5=0 factorises into (x+1)(2x^2-5)=0. There is one rational root, which is an integer, (x=-1) and 2 irrational roots.