(2)、 1+xy+x^2y^2= 1+xy( 1+xy)

Because xy in xy( 1+xy) is both a polynomial about X and Y, and (1+xy) is both a polynomial about X and a polynomial about Y, it cannot be expressed as c(x)d(y), so 1+XY+X 2Y.

The following is the definition of polynomial:

Anx is called a polynomial:

anx+an- 1x+…+a2x+a 1x+A0(an≠0)( 1)

The highest term or the first term. An is called the first coefficient, and the nonnegative integer n is called the degree of polynomial (1).

A polynomial whose highest degree term is a zeroth degree term, that is, the degree of a(a≠0) is zero, which is called a zeroth degree polynomial.

So x 0 =1is the zeroth polynomial of x, and b (y) = y 0 =1is the zeroth polynomial of y.

So this order a (x) =1c (x) = XB (y) =1d (y) = y completely conforms to the definition of polynomial, that is to say, there is no problem at all.