Problem 4
A point in the plane with a Cartesian coordinate system is called a mixed point if one coordinate is rational and the other is irrational. Find all polynomials with real coefficients whose graphs contain no mixed point.
Step 3 of 7: Normalize the polynomial
Detailed analysis
After a nonzero rational change of scale in the input and output, which preserves rational versus irrational numbers, we may assume the polynomial has integer coefficients and is monic. This does not change the graph condition.