Which of the following is a linear polynomial in x?
Answer and explanation
Correct answer: 5x-9
The governing concept is the degree of a nonzero polynomial. A linear polynomial has degree exactly 1, meaning the highest power of the variable with a nonzero coefficient is x^1. In option A, 5x-9 has highest exponent 1 and therefore is linear. Option B, x^2-9, has degree 2 and is quadratic. Option C is a nonzero constant polynomial, whose degree is 0. Option D, x^3+x, has highest exponent 3 and is cubic, even though it also contains a linear term. Thus option A is the only correct answer. The classification depends on the greatest exponent, not simply on whether the expression contains x or has only a few terms. The nonzero coefficient of x in 5x-9 confirms its degree is exactly one.
Frequently asked questions
What is the correct answer to this question?
5x-9
Why is this the correct answer?
The governing concept is the degree of a nonzero polynomial. A linear polynomial has degree exactly 1, meaning the highest power of the variable with a nonzero coefficient is x^1. In option A, 5x-9 has highest exponent 1 and therefore is linear. Option B, x^2-9, has degree 2 and is quadratic. Option C is a nonzero constant polynomial, whose degree is 0. Option D, x^3+x, has highest exponent 3 and is cubic, even though it also contains a linear term. Thus option A is the only correct answer. The classification depends on the greatest exponent, not simply on whether the expression contains x or has only a few terms. The nonzero coefficient of x in 5x-9 confirms its degree is exactly one.
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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