Which of the following expressions are polynomials in one variable and which are not?
State reasons for your answer. (i) (ii) and (iii) .
Step 1: (i): Determine whether the expression is a polynomial in one variable or not.
A polynomial is defined as a mathematical equation with one or more terms made up of variables, constants, and exponents that are mixed using operations like addition, subtraction, multiplication, and division.
The expression can be written as follows:
In the given expression, is the variable that has powers , which are whole numbers.
Hence, is a polynomial in one variable.
Step 2: (ii) Determine whether the expression is a polynomial in one variable or not.
The expression can be written as follows:
In the given expression, is the variable that has power , which is not a whole number.
Hence, is not a polynomial in one variable.
Step 3: (iii): Determine whether the expression is a polynomial in one variable or not.
In the given expression, are the variables that have powers , which are whole numbers.
Hence, is not a polynomial in one variable.