Which statement about the degree of the zero polynomial 0 is correct?
Answer and explanation
Correct answer: The degree is not defined
The governing concept is the degree of a polynomial, defined as the greatest exponent of x having a nonzero coefficient. The zero polynomial has every coefficient equal to zero, so it has no nonzero term and therefore no greatest exponent under the usual school-level definition. Its degree is consequently not defined. This must be distinguished from a nonzero constant polynomial such as 5, whose only nonzero term is 5x⁰ and whose degree is 0. Thus option A is incorrect because it confuses the zero polynomial with a nonzero constant; options B and D assign exponents without a corresponding nonzero term. Option C correctly states the standard result.
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What is the correct answer to this question?
The degree is not defined
Why is this the correct answer?
The governing concept is the degree of a polynomial, defined as the greatest exponent of x having a nonzero coefficient. The zero polynomial has every coefficient equal to zero, so it has no nonzero term and therefore no greatest exponent under the usual school-level definition. Its degree is consequently not defined. This must be distinguished from a nonzero constant polynomial such as 5, whose only nonzero term is 5x⁰ and whose degree is 0. Thus option A is incorrect because it confuses the zero polynomial with a nonzero constant; options B and D assign exponents without a corresponding nonzero term. Option C correctly states the standard result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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