In the context of polynomials in $x$, is $18$ a polynomial?

• A. No, because polynomials cannot have a constant term.
• B. Yes, because $18$ is a constant polynomial (degree $0$).
• C. No, because the coefficient $18$ is not a fraction.
• D. No, because polynomials must include the variable $x$.

Answer: (B)

Verified step by step guidance

1. Recall the definition of a polynomial in the variable \(x\): it is an expression consisting of terms in the form \(a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0\), where each \(a_i\) is a real number (coefficient) and \(n\) is a non-negative integer.
2. Understand that a polynomial can have terms with variables raised to whole number powers, but it can also be a constant term alone, which corresponds to the case where the degree \(n = 0\).
3. Recognize that the number 18 can be written as \$18 \cdot x^0\(, since \)x^0 = 1\( for any \)x \neq 0$.
4. Since \$18$ fits the form of a polynomial with degree 0 and a real coefficient, it qualifies as a polynomial, specifically a constant polynomial.
5. Therefore, the correct reasoning is that 18 is a polynomial because it is a constant polynomial of degree 0, and polynomials do not require the variable \(x\) to be explicitly present.