How is a linear polynomial identified?
Answer and explanation
Correct answer: By highest power 1
The governing concept is the degree of a polynomial. The degree is the greatest exponent of the variable whose coefficient is not zero. A polynomial is called linear when its degree is exactly 1; it may have one term, two terms, or more terms, provided the greatest nonzero exponent is 1. For example, 3x+5 and -7x are linear polynomials, whereas x^2+1 has degree 2 and is quadratic. Thus option C correctly identifies a linear polynomial by its highest power being 1. Power 0 describes a nonzero constant polynomial, power 2 describes a quadratic polynomial, and the number of terms does not determine whether a polynomial is linear.
Frequently asked questions
What is the correct answer to this question?
By highest power 1
Why is this the correct answer?
The governing concept is the degree of a polynomial. The degree is the greatest exponent of the variable whose coefficient is not zero. A polynomial is called linear when its degree is exactly 1; it may have one term, two terms, or more terms, provided the greatest nonzero exponent is 1. For example, 3x+5 and -7x are linear polynomials, whereas x^2+1 has degree 2 and is quadratic. Thus option C correctly identifies a linear polynomial by its highest power being 1. Power 0 describes a nonzero constant polynomial, power 2 describes a quadratic polynomial, and the number of terms does not determine whether a polynomial is linear.
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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