- Before you begin to understand the difference between a polynomial and a monomial, you need to understand that, in the context of algebra, they are the same thing. The terms are interchangeable, to a degree. Just as a square is also a specific form of a rectangle, a monomial is also a polynomial. Though all squares may also be called rectangles, all rectangles are not squares. Similarly, all monomials may also be called polynomials, though not all polynomials may be called monomials.
- The first step in learning to distinguish between polynomials and monomials is to understand the difference between the prefixes in the words. Both words have the term "nomial" in common. What is different about the words is the part at the beginning, "poly" and "mon." "Poly" comes from the Greek language and means "many." "Mono" is also Greek and means "singular," or "one."
- "Nomial" most likely comes from the Latin "nomen," for "name." In algebraic terms, nomial refers to the operations in the equation. If "mono" is one, then "monomial" refers to a function with a singular operation or number, such as 4, or 2a, or 3(5)xb. In each instance, even though a function is being performed, only one number is named. Similarly, 4/2 or 5~3 are also monomials.
- Understanding that "poly" means "many," or at least "more than one," you can see that a polynomial refers to multiple operations in an equation, such as a2b3 + 20cb - 10a = x, or a(3 x 10) - 13 + 27xn. In each of the described cases, there are multiple functions describing multiple numbers to be added and subtracted. Compared side by side, it should be simple to see the difference between 20n, a monomial, and 10n + 10, a polynomial. Polynomials may be designated as monomials (one function), binomials (two functions), trinomials (three functions) and so on, or may simply be referred to as polynomials.
A Rose is a Rose
From Many, One
Monomial
Polynomials
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