Q22. - Algebra 1

Question

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

Explain your reasoning.

$3a^4$

Step-by-Step Solution

Answer

Yes, the expression $3a^4$ is a monomial.

Step 1. State the concept of ‘monomial’.

A polynomial which contains only one non-zero single term is called a monomial. A monomial consists either one variable or a constant or products of more than one variable with a coefficient along with the exponents as a whole numbers.

 

Note: A monomial cannot have a variable in the denominator.The variable in the denominator is considered as second term.

Step 2. State the parts of monomial expression.

The different parts of the monomial expression are given as follows:

 

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

 

Variable: The alphabets present in the monomial expression are called as variables

 

Literal part: All the other parts except the coefficient, are called the literal part of the expression.  

 

Degree: The sum of the powers of the variables in the expression is the degree of the expression.

 

Example: $5a^2{b}^3$ is a monomial expression.

 

Here, see that the coefficient is 5.

 

Variables in the given expression are a and b.

 

$$\begin{gathered} \text{Degree\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}the\hspace{0.17em}\hspace{0.17em}monomial\hspace{0.17em}\hspace{0.17em}expression}=\text{\hspace{0.17em}degree\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em} \hspace{0.17em}}a+\text{degree\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em} }b \\ =2+3 \\ =5 \end{gathered}$$

 

The literal part of the expression is $a^2{b}^3$.

Step 3. State the conclusion.

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

 

The expression $3a^4$ contains a constant 3 and a variable ‘a’.

 

By the definition of monomial, $3a^4$ is considered as one single term where 3 is the coefficient and $a^4$ is the literal part.

 

Hence, $3a^4$ is a monomial.