Q4. - Algebra 1

Question

Determine whether the given expression is a monomial. Write yes or no.

Explain your reasoning.

$-15g^2$

Step-by-Step Solution

Answer

Yes, the expression $-15g^2$ is a monomial.

Step 1. State the concept of ‘monomial’.

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 $x{y}^2$.

Step 3. State the conclusion.

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

 

The expression $-15g^2$ is a non-zero term that contains a constant 15 and a variable g.

 

By the definition of monomial, $-15g^2$ is considered as one single term.

 

Hence, $-15g^2$ is a monomial.