# 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?

Nov 20, 2017

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.

#### Explanation:

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"
$x$

$3 y$

$7 m \times 22$

${\left(4 x - 2\right)}^{2} \div 3 {\left(6 x - 13\right)}^{6}$
.........................

Terms are separated from each other by addition or subtraction.
Here are expressions with two terms:
a + 3

$45 {x}^{2} - {m}^{3}$

${\left(4 x - 2\right)}^{2} \div 3 {\left(6 x - 13\right)}^{6} + \left(a + x\right) \left(a - x\right)$

$\leftarrow$------ one term ----- $\rightarrow$ + $\leftarrow$another$\rightarrow$
.........................

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
$3 {s}^{3}$

a binomial if it has exactly 2 terms
$2 x + 3$

a trinomial if it has exactly 3 terms
${x}^{2} + 6 x + 9$
1 . . . . .2 . . . 3 $\leftarrow$ (the number of terms is 3)

a polynomial if it has more than 3 terms
(But expressions with 1, 2, or 3 terms are also still called polynomials.)

$m$ $\leftarrow$ monomial or polynomial

$x - 3$ $\leftarrow$ binomial or polynomial

$6 {y}^{3} - 9 {y}^{2} + 3 y$ $\leftarrow$ trinomial or polynomial

$8 {m}^{3} + 3 {m}^{2} - 7 m + 3$ $\leftarrow$ polynomial
. 1 . . . . . .2 . . . . . 3 . . . .4 $\leftarrow$ (the number of terms is 4)