Question

Which polynomial has only one term?
a) binomial
b) multinomial
c) trinomial
d) monomial

Answer 1

Hint: A polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Complete answer:
Polynomials can be classified on the basis of the number of terms it contains. If it has only one term then it is called a monomial. If it has two terms it is called a binomial. If it has three terms then it is called a trinomial. If the polynomial contains more than three terms then it is called a multinomial.
So, the polynomial with only one term is called a monomial. For example; \[5{x^3},{x^2},2x\] are examples of monomials.
Therefore, the correct option is (d).

Additional details:
The \[x\] occurring in a polynomial is commonly called a variable or an indeterminate. When the polynomial is considered as an expression, \[x\] is a fixed symbol which does not have any value (its value is "indeterminate"). However, when one considers the function defined by the polynomial, then \[x\] represents the argument of the function, and is therefore called a "variable". A polynomial \[P\] in the indeterminate \[x\] is commonly denoted either as \[P\] or as \[P\left( x \right)\].

Note: One major mistake that many students make is that while classifying a given expression as a polynomial, they do not see whether the exponents of the terms in the expression are non-negative or not. If the exponent of any of the terms in the given expression is negative then that expression cannot be considered as a polynomial.