Which of the following is not a polynomial in \(x\)?
Answer and explanation
Correct answer: \(\frac{5}{x^2}+1\)
In \(\frac{5}{x^2}+1=5x^{-2}+1\), the power of \(x\) is \(-2\). In a polynomial, the powers of the variable must be non-negative integers, so this expression is not a polynomial. Option D, \(7x+8\), is a linear polynomial because the power of \(x\) is 1. Exam tip: when the variable appears in the denominator, its power becomes negative, which generally disqualifies the expression from being a polynomial.
Frequently asked questions
What is the correct answer to this question?
\(\frac{5}{x^2}+1\)
Why is this the correct answer?
In \(\frac{5}{x^2}+1=5x^{-2}+1\), the power of \(x\) is \(-2\). In a polynomial, the powers of the variable must be non-negative integers, so this expression is not a polynomial. Option D, \(7x+8\), is a linear polynomial because the power of \(x\) is 1. Exam tip: when the variable appears in the denominator, its power becomes negative, which generally disqualifies the expression from being a 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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