Which of the following expressions is a polynomial in the single variable \(z\)?
Answer and explanation
Correct answer: \(z^4-2z+1\)
In \(z^4-2z+1\), only the variable \(z\) occurs, and its exponents 4, 1, and 0 are non-negative integers. Therefore, it is a polynomial in one variable, \(z\). Options B and C contain a negative power or a variable in the denominator, while option D contains two variables, \(z\) and \(w\). Exam tip: the powers of the variable in a polynomial must be non-negative integers.
Frequently asked questions
What is the correct answer to this question?
\(z^4-2z+1\)
Why is this the correct answer?
In \(z^4-2z+1\), only the variable \(z\) occurs, and its exponents 4, 1, and 0 are non-negative integers. Therefore, it is a polynomial in one variable, \(z\). Options B and C contain a negative power or a variable in the denominator, while option D contains two variables, \(z\) and \(w\). Exam tip: the powers of the variable in a polynomial must be non-negative integers.
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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