Question

Degree of polynomial 5 is _____
A.1
B.2
C.0
D.Not defined.

Answer 1

Hint: We know the definition of a polynomial and its degree. We know that the polynomial is in form \[P(x) = {a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3} + - - - + {a_n}{x^n}\]. Degree of a polynomial is the highest or the greatest degree exponent term in a polynomial. We also know if any non-zero number raised to the power of zero is equal to one.

Complete step-by-step answer:
We know the degree of the polynomial is the highest degree of a variable in the polynomial. That is it indicates the highest exponential power in the polynomial (excluding the coefficients).
We need to find the degree of a polynomial 5.
5 can be written as \[ \Rightarrow 5 \times 1\].
We know that a non-zero number raised to the power of zero is equal to one.
That is. \[{x^0} = 1\], where ‘x’ is a variable.
Then we have,
\[ \Rightarrow 5 \times {x^0}\].
We can see that the exponential power of term ‘x’ is zero and which is the greatest exponential.
Hence, the degree of the polynomial 5 is 0.
So, the correct answer is “Option C”.

Note: One of the important notes is zero power zero is not equal to 0. That is \[{0^0} \ne 1\]. In fact \[{0^0} = 0\]. There are different types of polynomials. Those are Constant polynomial, Linear polynomial, Quadratic polynomial, Cubic polynomial, Bi-quadratic polynomial and so on. In our given problem, 5 is a Constant polynomial. Degree of a constant polynomial is 1. The polynomial is of degree ‘n’ is given by
\[P(x) = {a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3} + - - - + {a_n}{x^n}\] .