Which option gives the correct general condition for a polynomial?
Answer and explanation
Correct answer: The powers of the variable are zero or positive integers
The governing concept is the general definition of a polynomial in one variable. Its form may be written as a₀ + a₁x + a₂x² + ... + aₙxⁿ, where the exponents 0, 1, 2, ..., n are non-negative integers and the coefficients are permitted numbers, commonly real numbers at this level. Therefore option C states the correct general condition. Negative exponents correspond to reciprocal or denominator forms and are excluded. Fractional exponents produce radical-type expressions and are also excluded. A variable does not have to be in a denominator; in fact, placing it there usually creates a negative power. Hence options A, B, and D describe conditions incompatible with the standard polynomial definition.
Frequently asked questions
What is the correct answer to this question?
The powers of the variable are zero or positive integers
Why is this the correct answer?
The governing concept is the general definition of a polynomial in one variable. Its form may be written as a₀ + a₁x + a₂x² + ... + aₙxⁿ, where the exponents 0, 1, 2, ..., n are non-negative integers and the coefficients are permitted numbers, commonly real numbers at this level. Therefore option C states the correct general condition. Negative exponents correspond to reciprocal or denominator forms and are excluded. Fractional exponents produce radical-type expressions and are also excluded. A variable does not have to be in a denominator; in fact, placing it there usually creates a negative power. Hence options A, B, and D describe conditions incompatible with the standard polynomial definition.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Definition of a Polynomial.
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