Which of the following is a polynomial in one variable but not a linear polynomial?
Answer and explanation
Correct answer: \(x^2+2x+3\)
In \(x^2+2x+3\), the powers of \(x\) are 2, 1, and 0, all of which are non-negative integers; hence it is a polynomial. Its highest power is 2, so it is a quadratic polynomial, not a linear one. Option A has degree 1 and is linear, while option C contains \(x^{-1}\) and option D contains \(x^{1/2}\), so neither is a polynomial. Exam tip: in a polynomial, the variable can have only non-negative integer exponents such as 0, 1, 2, and so on.
Frequently asked questions
What is the correct answer to this question?
\(x^2+2x+3\)
Why is this the correct answer?
In \(x^2+2x+3\), the powers of \(x\) are 2, 1, and 0, all of which are non-negative integers; hence it is a polynomial. Its highest power is 2, so it is a quadratic polynomial, not a linear one. Option A has degree 1 and is linear, while option C contains \(x^{-1}\) and option D contains \(x^{1/2}\), so neither is a polynomial. Exam tip: in a polynomial, the variable can have only non-negative integer exponents such as 0, 1, 2, and so on.
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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