Question

Determine whether the given expression is a monomial or not.

$\frac{xy{z}^2}{2}$

Short answer

The expression$\frac{xy{z}^2}{2}$ is a monomial.

Step-by-step solution

Step 1. State the concept of ‘monomial expression’.

A monomial is a type of polynomial, which is an algebraic expression having only a non-zero single term. Monomial consists of only a single term which makes it easy to do the operation of addition, subtraction and multiplication. It consists of either only one variable or one coefficient or product of a variable and a coefficient with exponents as whole numbers, which represent only one term, unlike binomial and trinomial, which consist of two and three terms respectively. It cannot have a variable in the denominator.

Step 2. State the parts of monomial expression.

The different parts present in the monomial expression are:

Variable: The letters present in the monomial expression.

Coefficient:The number which is multiplied by the variable in the expression.

Degree:The sum of the exponents present in the expression.

Literal part:The alphabets which are present along with the exponent value in the expression.

Example:$4x{y}^2$is a monomial expression.

Here,the coefficient is 4.

Variables are x and y.

The degree of the monomial expression$=1+2=3$

The literal part is role="math" $x{y}^2$.

Step 3. State the conclusion.

From the definition a monomial expression must contain only one non-zero term.

The expression$\frac{xy{z}^2}{2}$contains only single term.

Note: Even though it contains three variables in numerator$x,y,z$and a constant 2 in denominator all those are considered as one single term by the definition of monomial.

Hence, $\frac{xy{z}^2}{2}$is a monomial expression.