Which of the following expressions is a polynomial in \(x\)?
Answer and explanation
Correct answer: \(x^2+\frac{1}{3}x+2\)
In a polynomial, the powers of the variable must be non-negative integers. In option B, the powers of \(x\) are 2, 1, and 0, and \(\frac{1}{3}\) is a valid real coefficient; therefore, it is a polynomial. Options A and D contain fractional powers, while option C has \(x\) in the denominator, giving it a negative power. Exam tip: an expression is not a polynomial if the variable has a fractional or negative exponent.
Frequently asked questions
What is the correct answer to this question?
\(x^2+\frac{1}{3}x+2\)
Why is this the correct answer?
In a polynomial, the powers of the variable must be non-negative integers. In option B, the powers of \(x\) are 2, 1, and 0, and \(\frac{1}{3}\) is a valid real coefficient; therefore, it is a polynomial. Options A and D contain fractional powers, while option C has \(x\) in the denominator, giving it a negative power. Exam tip: an expression is not a polynomial if the variable has a fractional or negative exponent.
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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