Question

Define a constant polynomial and give its degree.

Answer 1

Hint: We first try to form the general form of n-degree polynomial $ {{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+......+{{a}_{n}}{{x}^{n}} $ . We then express the constant polynomial and find its general form. Then using the constant value 2 in that form, we find the power value for the term of the constant.

Complete step-by-step answer:
Any polynomial of variable $ x $ can be expressed as $ {{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+......+{{a}_{n}}{{x}^{n}} $ .
Every term in the expression has its own power value and the maximum of those numbers defines the degree of the whole polynomial.
Case in point for the above expression the height power value is $ n $ and therefore, the polynomial is of n-degree.
The only term without variable $ x $ is the constant term $ {{a}_{0}} $ . Its power value can be written as $ {{a}_{0}}={{a}_{0}}{{x}^{0}} $ as $ {{x}^{0}}=1 $ . This form is known as a constant polynomial where $ max\left( n \right)=0 $ .
Now we want to express the given constant polynomial 2 in the form of a polynomial.
We can write it as $ 2=2+0.x+0.{{x}^{2}}+......+0.{{x}^{n}} $ .
Therefore, all the coefficients form the variables other than the constant term is 0.
The maximum power value for existing variables of 2 is 0 which can be written as $ 2=2{{x}^{0}} $ .

Note: A polynomial is the parent term used to describe a certain type of algebraic expressions that contain variables, constants, and involve the operations of addition, subtraction, multiplication, and division along with only positive powers associated with the variables.