Question

The polynomial 8 is of degree?
$
  (a){\text{ 1}} \\
  (b){\text{ }}\dfrac{1}{2} \\
  (c){\text{ 8}} \\
  (d){\text{ 0}} \\
$

Answer 1

Hint – In this question use the concept that the degree of a polynomial is the highest power of its monomials terms or the highest power of the terms involving variables only, 8 can be written as $0{x^2} + 0x + 8 = 0$, use the definition along with this concept to get the answer.

Complete step-by-step answer:
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
For example: $a{x^2} + bx + c = 0$
It is a second degree quadratic equation.
So the given expression is a non-zero constant which is 8.
And we all know this is not a variable.
So for non-zero constants the degree is zero (0).
So 8 is polynomial of degree 0.
So this is the required answer.
Hence option (D) is correct.

Note – The key point here in definition was that only the non-zero variables terms need to be taken into consideration, just as we did for 8. The degree of a cubic polynomial is 3 as it is of the form $a{x^3} + b{x^2} + cx + d = 0$, and the highest power involving the variable term that is for x is 3.