A monomial is an algebraic expression consisting of the product of numbers or letters. A single number or letter is also called a monomial, and the product of fraction and letter is also called a monomial.
For example, 0, 1, x, a, 2xy and (ab)/2 are all monomials.
Polynomials are algebraic expressions composed of addition and subtraction of several monomials. Each monomial in a polynomial is called a polynomial term, and the highest degree of these monomials is the degree of this polynomial.
For example, x+2xy, a+b, (ab)/2-2xy are all polynomials.
There are no addition and subtraction operations in monomials, and polynomials are composed of addition and subtraction operations of several monomials. So the way to distinguish a monomial from a polynomial is to see if there are addition and subtraction operations in a formula.
Extended data:
The sum of finite monomials is called polynomial. A polynomial expressed by the sum of different kinds of monomials, in which the highest degree of monomials with non-zero coefficients is called the degree of the polynomial.
Polynomial addition refers to the addition of coefficients of similar items in polynomials, and the letters remain unchanged (that is, the similar items are merged). Polynomial multiplication means that each monomial in one polynomial is multiplied by each monomial in another polynomial, and then similar items are merged.
Set Fx{ 1, x2, ..., xn} from xn on x 1, x2, ..., f to a ring through polynomial addition and multiplication, which is an integral ring with unit elements.
Multivariate polynomials over fields also have uniqueness theorems of factorization.
Baidu encyclopedia-single item
Baidu encyclopedia-polynomial