The Difference between a Monomial and a Polynomial
by Deborah
(Hardin, KY)
Why is -2 a polynomial and -5 is a monomial? I do not understand the rationale behind this and my textbook is not clear. Also how can 0 be both?
Karin from Algebra Class Says:
Before we talk about Polynomials, I want you to think of Bread!
Bread is a very general term and there are a lot of different types of bread.
Bread
Rye
Wheat
White
We could call Rye bread just bread or we could be more specific and classify is as Rye.
This is exactly how Polynomials work:
Polynomial is the general term, but some polynomials can be classified in a more specific way.
A polynomial is any sum (or difference) of terms. A term is separated by a plus or minus sign (that's why the word sum is used).
Some polynomials can be classified more specifically as monomials, binomials, or trinomials.
Polynomials
Monomial (one term) - Examples: 4, 3x, 6xy, (notice there are no plus or minus signs.)
Binomial (two terms) - Examples: 3x + 2y (notice there is one plus sign)
Trinomial (three terms) - Examples: 3x+2y-4 (notice there are two plus/minus signs)
Anything with more terms than three is just classified as polynomial.
But monomials, binomials, and trinomials are also polynomials because Polynomial is the "bread" or general term.
So, to answer your question, -2, -5, and 0 are all polynomials (generally) but they can be classified further as monomials because they only have 1 term.
Hope this helps in your understanding.
Karin