How do you determine if #(5y^2)/x^2+4x# is a polynomial and if so, how do you identify if it is a monomial, binomial, or trinomial?
The expression is a polynomial with two terms.
That makes it a binomial.
Polynomials are algebraic expressions made up of one or more terms, which are addends.
The number of terms defines the name of the polynomial.
Polynomials are algebraic expressions made up of more than one "term."
A "term" is a cluster of numbers and letters that are connected to each other by multiplication and division.
These are all "terms"
Terms are separated from each other by addition or subtraction.
Here are expressions with two terms:
a + 3
You can tell if an expression is a monomial, a binomial, a trinomial, or a polynomial by counting the terms.
We give expressions with 1, 2, or 3 terms special names, but after that we stop counting and just say "polynomial."
Specific kinds of polynomials are called:
a monomial if it has exactly 1 term
a binomial if it has exactly 2 terms
a trinomial if it has exactly 3 terms
1 . . . . .2 . . . 3
a polynomial if it has more than 3 terms
(But expressions with 1, 2, or 3 terms are also still called polynomials.)
. 1 . . . . . .2 . . . . . 3 . . . .4
Here is more information about terms and polynomials