Question

The degree of constant polynomial is?
(a) 1
(b) 2
(c) 0
(d) 3

Answer 1

Hint: To solve this problem, we should know the basics of algebraic polynomials. Then we can use these basic results to find the correct option to this question. Further, we will use the fact that the degree of the polynomial is the largest exponent of a variable in the polynomial.

Complete step-by-step solution -

Before we begin to solve this problem, we first understand the basics of polynomials briefly. Basically, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. To explain, we do this through an example of a polynomial, we have ${{x}^{4}}-3{{x}^{3}}+5$ . Further, usual properties of commutativity, associativity and distributivity of addition and multiplication are still applicable to the polynomial equation. Now, coming back to the problem in hand, we need to find the degree of constant polynomial.
The degree of a polynomial is the largest exponent in the polynomial. For example, in case of ${{x}^{2}}{{y}^{3}}+{{x}^{4}}+xy$ , the degree of the polynomial is 2+3 = 5 (since, it is the highest exponent in the given polynomial). Now, a constant polynomial is one which is devoid of any variables (like x and y) and has only a constant term (which is a number). For example, 23, 45 or 66 are the examples of constant polynomials. For these examples, we can write them in the form 23 ${{x}^{0}}$ (since ${{x}^{0}}$ = 1). Thus, the degree of the constant polynomial is 0.
Hence, the correct answer is (c) 0.

Note: In the given problem, we can always represent a constant term in the form of ${{x}^{0}}$ , this greatly helps in representing the polynomial in the term of its familiar notation. Further, a polynomial can have as many number of variables as possible (thus, there can also be x,y and z terms in the polynomial equation).