What is the degree of a linear polynomial?
Answer and explanation
Correct answer: 1
The governing definition is that a linear polynomial in one variable has the form ax + b, where a is nonzero and b is a constant. The highest power of x that actually occurs is therefore x^1, so its degree is 1. For example, 4x − 7 is linear because the variable appears to the first power. A constant such as 5 has degree 0, while x^2 + 1 is quadratic and has degree 2. The number of terms does not determine degree; the greatest nonzero exponent does. Thus option C is correct. Option A describes a nonzero constant polynomial, and options B and D describe polynomials of higher degrees rather than a linear polynomial.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The governing definition is that a linear polynomial in one variable has the form ax + b, where a is nonzero and b is a constant. The highest power of x that actually occurs is therefore x^1, so its degree is 1. For example, 4x − 7 is linear because the variable appears to the first power. A constant such as 5 has degree 0, while x^2 + 1 is quadratic and has degree 2. The number of terms does not determine degree; the greatest nonzero exponent does. Thus option C is correct. Option A describes a nonzero constant polynomial, and options B and D describe polynomials of higher degrees rather than a linear polynomial.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.
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