Q25. - Algebra 1

Question

Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial.

$\frac{3x}{5y}$

Step-by-Step Solution

Answer

The given expression $\frac{3x}{5y}$ is not a polynomial.

Step 1. Write the definition of the polynomial.

A monomial is a number, a variable or the product of a number and one or more variables with non-negative integer exponents. The monomial has only one term.

 

A polynomial is a monomial or the sum of monomials, each called a term of the polynomial.

 

The polynomial having only one term is called a monomial.

 

The polynomial having two terms is called a binomial. That is binomial is sum of two monomials.

 

The polynomial having three terms is called a trinomial. That is trinomial is sum of three monomials.

Step 2. Determine whether each expression is a polynomial.

The given expression is $\frac{3x}{5y}$.

 

The given expression can be written as:

$$\begin{gathered} \frac{3x}{5y}=\frac{3}{5}\times \frac{x}{y} \\ =\frac{3}{5}\times x\times y^{-1} \\ =\frac{3}{5}x{y}^{-1} \end{gathered}$$

Therefore, the expression is $\frac{3}{5}x{y}^{-1}$.

 

It can be noticed that each term of the expression is the product of a number and variables with negative integer exponents.

 

Therefore, the term of the expression is not a monomial.

 

As, the expression is not a monomial. Therefore, the given expression is not a polynomial.