Page "Polynomial" Paragraph 31

A formal quotient of polynomials, that is, an algebraic fraction where the numerator and denominator are polynomials, is called a " rational expression " or " rational fraction " and is not, in general, a polynomial.

Division of a polynomial by a number, however, does yield another polynomial.

For example, x < sup > 3 </ sup >/ 12 is considered a valid term in a polynomial ( and a polynomial by itself ) because it is equivalent to 1 / 12x < sup > 3 </ sup > and 1 / 12 is just a constant.

When this expression is used as a term, its coefficient is therefore 1 / 12.

For similar reasons, if complex coefficients are allowed, one may have a single term like ( 2 + 3i ) x < sup > 3 </ sup >; even though it looks like it should be expanded to two terms, the complex number 2 + 3i is one complex number, and is the coefficient of that term.

The expression 1 /( x < sup > 2 </ sup > + 1 ) is not a polynomial because it includes division by a non-constant polynomial.

The expression ( 5 + y )< sup > x </ sup > is not a polynomial, because it contains a variable used as exponent.