Question

Can someone help me understand exactly what a polonomial is? Please explain it, not a link please!

Answer 1

A polynomial is made up of the sum of monomials.

Monomials have 1 term. Like 8x^2y^2

You can also have a fraction in a monomial BUT as long as the denominator is a number not a variable, it is considered a monomial

\(\ \frac{8x^2}{5}\) is a monomial
\(\ \frac{2x^2}{y}\) is not a monomial because \(\ \frac{2x^2}{y} = 2x^2y^{-1}\) and the variable should not have a negative exponent

Now, if a polynomial is made up of two monomials, it is called a binomial
And if it is made up of three monomials, it is called a trinomial.
If it's made up of more terms, you just call it a polynomial that has a degree of whatever the highest degree of the monomial is

mhmm, does that make sense? :)

Answer 2

I can go more in to it, and more around it

I just taught this concept the other day to my students xD

Answer 3

Makes perfect since. Can you go more into the degrees and such?

Answer 4

Degree of a monomial is adding the power of each of the VARIABLES

Degree of a polynomial is the the highest degree there is of one of the monomials


the degree of 8x^2y is 3
x^2 and y^1
2 + 1 = 3
the degree is 3


the degree of 8x^2 + 2x + 1
8x^2 has a degree of 2
2x has a degree of 1 because x^1
and 1 has a degree of 0 because 1 * x^0 = 1 * 1 = 1

the highest degree of a monomial in the polynomial is 2, which means the degree is 2