Question

The difference between an algebraic expression and a polynomial is:
A.The exponents of polynomial terms are whole numbers while that of algebraic expressions are not.
B.The exponent of algebraic expression terms are whole numbers while that of polynomials are not.
C.The constant term is absent in algebraic expression while it is present in polynomials.
D.None of the above

Answer 1

Hint: We have to define an algebraic expression and a polynomial in order to differentiate between the two , also it's advisable to give several examples of each so that the difference can be expressed in a better way and understood more clearly.

Complete step-by-step answer:
An expression that consists of constants, variable and algebraic operations like addition, subtraction, etc. is called an algebraic expression.
In an algebraic equation, there is some unknown variable and the defined constant with the variable is known as the coefficient and there can also be a constant defined value in the equation. For example, $2x+4$
In this algebraic equation, x is the unknown variable, 2 is the coefficient of x and 4 is the constant. A polynomial is a subtype of algebraic expression but is a little different from it.
The exponents of a polynomial equation are whole numbers only, whereas an algebraic expression can have any real number as the exponent.
For example, $x^{\sqrt{2}}$ is an algebraic expression in which the exponent is ${\displaystyle \frac{1}{2}}$ but a polynomial cannot take this kind of values as the exponent.
Therefore, the correct answer is that the exponents of polynomial terms are whole numbers while that of algebraic expressions are not.
So, the correct answer is “Option A”.

Note: There are three types of algebraic expressions –
Monomial expression – It is an algebraic expression that has only one term. For example, $3x^2,6xy,9x,2y$
Binomial expression – An algebraic expression having two unlike terms is called a binomial expression. For example, $3xy+9,y^3+xyz$
Polynomial expression – An algebraic expression having more than two unlike terms is called a polynomial expression. For example, $x^2+y^2+2z,x^3+6x+9$