Question

Degree of a constant term is
(A) \[1\]
(B) \[0\]
(C) \[2\]
(D) Not defined

Answer 1

Hint: In this question, we have to choose the correct option from the given particular options that satisfies the given condition. We need to first consider the definition of constant term and degree. By using the definition we will get the final answer. Then choose the correct option which is actually appropriate for the required.

Complete step-by-step answer:
We need to find out what is the degree of a constant term from the given options.
Considering the definition we have,
Degree of a term:
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's 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.
Constant term:
In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables.
For example if \[a{x^2} + bx + c\] is a polynomial then c is the constant term.
In a constant term the power of the variable is zero.
Since, \[c = c \times 1 = c \times {x^0}\]
So, its degree is zero.

Therefore (B) is the correct option.

Note: We have to mind that, for a univariate polynomial, the degree of the polynomial is simply the highest exponent occurring in the polynomial.
For example, the polynomial \[5{x^2}{y^3} + 9x - 6\] which can also be written as \[5{x^2}{y^3} + 9{x^1}{y^0} - 6{x^0}{y^0}\] has three terms. The first term has a degree of \[5\] (the sum of the powers \[2\& 3\]), the second term has a degree of one, and the last term has a degree of zero. Therefore, the polynomial has a degree of \[5\], which is the highest degree of any term.