MathDB

If the polynomials

f(x)

and

g(x)

are written on a blackboard then we can also write down the polynomials

f(x)\pm g(x), f(x)g(x), f(g(x))

and

cf(x)

, where

c

is an arbitrary real constant. The polynomials

x^3 - 3x^2 + 5

and

x^2 - 4x

are written on the blackboard. Can we write a nonzero polynomial of the form

x^n - 1

after a finite number of steps? Justify your answer.

Problem Statement