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Answer: The correct answer for the degree of the Zero Polynomial is option C. Not Defined
Complete Answer:
Option A. 1: The degree of a polynomial is determined by the highest power of xxx with a non-zero coefficient. For the zero polynomial, all coefficients are zero, meaning there is no term with a non-zero power of xxx. Thus, it does not have a degree of 1.
Option B. 0: A polynomial with the degree 0 is a constant polynomial (like 555 or −3-3−3), which has no variable xxx. The zero polynomial is not a constant polynomial; it doesn’t represent any value, so its degree is not 0.
Option C. Not defined: The zero polynomial is a polynomial in which all coefficients are zero (e.g., 0xn+0xn−1+⋯+00x^n + 0x^{n-1} + \dots + 00xn+0xn−1+⋯+0). Since it has no non-zero terms, it does not have the highest power of xxx, and thus, its degree is considered not defined.
Option D. Any natural number: The degree of a polynomial refers to the highest exponent of xxx. Since the zero polynomial has no non-zero terms, it doesn’t have any degree, and thus it cannot have a degree of any natural number.
Hence, the correct choice is C. Not defined.
What is a Polynomial?
A polynomial is a type of mathematical expression made up of terms that are connected by addition or subtraction. Each term in a polynomial consists of a number (called a coefficient) and a variable (usually xxx) raised to a power (called the exponent).
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