Which of the following expressions is a polynomial in \(t\)?
Answer and explanation
Correct answer: \(4t^3-\frac{1}{2}t+7\)
In a polynomial, the powers of the variable must be non-negative integers, while the coefficients may be real numbers. In option C, the powers of \(t\) are 3, 1, and 0, so it is a polynomial. Option A contains \(\sqrt{t}=t^{1/2}\), option B contains the negative power \(t^{-2}\), and option D has the variable in the denominator; hence, they are not polynomials. Exam tip: check the powers of the variable first—fractional or negative powers make an expression non-polynomial.
Frequently asked questions
What is the correct answer to this question?
\(4t^3-\frac{1}{2}t+7\)
Why is this the correct answer?
In a polynomial, the powers of the variable must be non-negative integers, while the coefficients may be real numbers. In option C, the powers of \(t\) are 3, 1, and 0, so it is a polynomial. Option A contains \(\sqrt{t}=t^{1/2}\), option B contains the negative power \(t^{-2}\), and option D has the variable in the denominator; hence, they are not polynomials. Exam tip: check the powers of the variable first—fractional or negative powers make an expression non-polynomial.
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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