Question

Write the degree of the given polynomials.
i. \[\sqrt{5}\]
ii. \[x^{0}\]
iii. \[x^{2}\]

Answer 1

Hint: In this question, we need to write the degree of the given polynomial. First we need to know about the degree of the polynomial. The degree of the polynomial is defined as the highest power of the variable term in the given polynomial. That is we need to see the highest power in the variable term of the given polynomial.

Complete step by step answer:
We need to find the degree of the given polynomial.
Given,
i. \[\sqrt{5}\]
We know that \[\sqrt{5}\] is a constant term. In constant polynomials, the highest degree is zero. Since the constant polynomial has no variables ,it has zero degree of polynomial.
Therefore from this we can conclude that the degree of the polynomial \[\sqrt{5}\] is \[0\].
ii. \[x^{0}\]
We know that any number power \[0\] is \[1\] . From this we can rewrite \[x^{0}\] as \[1\]. In constant polynomials, the highest degree is zero. Since the constant polynomial has no variables ,it has zero degree of polynomial.
Thus the degree of the polynomial \[x^{0}\] is \[0\].
iii. \[x^{2}\]
A polynomial with its highest degree \[2\] is known as quadratic polynomial. Since the given polynomial is a quadratic polynomial with power \[2\], the degree of the polynomial is \[2\] .
Thus the degree of the polynomial \[x^{2}\] is \[2\].

Note:
An algebraic expression which is built up with integers, constants, variables and mathematical operations (addition, subtraction, multiplication, division etc… ) is known as polynomial. In mathematics, a symbol (letter) which doesn’t have a value is called a variable. Similarly which has a fixed value is called constant.