Which polynomial in x has degree 0?
Answer and explanation
Correct answer: 12
The governing definition states that every non-zero constant polynomial has degree 0, because it can be written as a constant times x^0 and contains no higher power of x. Option A, the polynomial 12, is non-zero and constant, so its degree is 0. The polynomial x + 12 has highest exponent 1 and therefore degree 1. The polynomial x^2 + 12 has highest exponent 2 and therefore degree 2. The zero polynomial in option D is special: its degree is generally left undefined in school-level algebra because it has no highest non-zero power. Thus option D is not a second answer, and option A is the only unambiguous correct choice. The non-zero condition is essential when identifying a constant polynomial of degree zero.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The governing definition states that every non-zero constant polynomial has degree 0, because it can be written as a constant times x^0 and contains no higher power of x. Option A, the polynomial 12, is non-zero and constant, so its degree is 0. The polynomial x + 12 has highest exponent 1 and therefore degree 1. The polynomial x^2 + 12 has highest exponent 2 and therefore degree 2. The zero polynomial in option D is special: its degree is generally left undefined in school-level algebra because it has no highest non-zero power. Thus option D is not a second answer, and option A is the only unambiguous correct choice. The non-zero condition is essential when identifying a constant polynomial of degree zero.
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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