Question

What is the degree of the polynomial $ p\left( x \right) = 5 $ ?
(A) $ 5 $
(B) $ 1 $
(C) $ 0 $
(D) None of these

Answer 1

Hint: To find the degree of a given polynomial, we will observe the greatest power of a variable. Also observe the coefficient of the greatest power of variables. The coefficient of the greatest power of variables should be non-zero.

Complete step-by-step answer:
Here the given polynomial is $ p\left( x \right) = 5 $ . This polynomial is called a constant polynomial because the coefficient of $ {x^n} $ is zero for $ n \geqslant 1 $ . In simple words, there is no variable in the given polynomial and there is only one term which is constant. This polynomial can be written as $ p\left( x \right) = 5{x^0} $ because the value of $ {x^0} $ is equal to $ 1 $ . In this polynomial, $ x $ is the variable. Here we can see that the coefficient is $ 5 $ and the power of $ x $ is $ 0 $ . So, we can say that the greatest power of variable $ x $ is $ 0 $ and its coefficient is non-zero.
The degree of the polynomial is the greatest power of the variable. Therefore, the degree of the polynomial $ p\left( x \right) = 5 $ is $ 0 $ . Hence, option C is correct.

So, the correct answer is “Option C”.

Note: A polynomial which contains only one term is called a monomial. A polynomial which contains two terms is called a binomial. A polynomial which contains three terms is called trinomial. The degree of the polynomial is always a non-negative integer. To find the degree of polynomial, first arrange the variable in descending order of their powers. This is called the standard format. In this example, the degree of the polynomial is $ 0 $ . So, we can say that it is a zero degree polynomial (constant polynomial). Coefficients of the variable can be any real number.