eli5 What is a monomial, binomial, polynomial and multinomial?

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I don’t understand very well, what happens if I have an expression with degree of algebraic terms a real number or a natural number? how are each called?

and for example, the number 137 is a term? is an arithmetic expression?

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Those names just refer to the number of terms in an expression. “4x” is a monomial. “4x+3” is a binomial, etc. Any binomial, trinomial, or more can be described as a polynomial because that just means several terms. I’ve never actually heard multinomial but “poly-” and “multi-” both mean many, just with different word origins.

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X

3X^2 ( read as 3 times X squared)

Are all monomials. There is One (mono) element in the expression.

2X + 7

X^2 – 1 (X squared minus one)

Are all binomials. There are 2 (bi) elements in each expression.

Poly and multi means many, so a polynomial or multinomial just has many elements in each expression. Like these:

X^2 + 2X + 1

X^27 – 3X^20 + X^2 + 1

(edit to fix formatting. Sorry for the delay, I lost service. In town. SMH, the joys of living nowhere)