Which of the following is a polynomial?

(This question has multiple options)

see full answer

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2 x

x^{2} + y^{- 2} - 2 z^{2}

5 x^{3} y^{2} z^{3}

x + x^{2} + x^{3} + x^{4}

answer is A.

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Detailed Solution

Polynomial is the expression which consist of unknown variables, coefficients of the variables and constant terms.
The exponent of the variable in a polynomial should be whole number and non-negative integer.

1) 2 x

It is an expression with a single variable, x, that uses the multiplication operation and has an exponent of 1, a non-negative integer.
So, it is an polynomial.

2) x^{2} + y^{- 2} - 2 z^{2}

It is an expression with a single variable, x, that uses the multiplication operation and has an exponent of 1, a non-negative integer.
Hence

x^{2} + y^{- 2} - 2 z^{2}

(option 2) is not a polynomial.

3) 5 x^{3} y^{2} z^{3}

It is an equation with three variables (x, y, and z), and it only uses the multiplication operation. The exponents of the variables x, y, and z are non-negative integers and are 3, 2, and 3 correspondingly.
Hence,

5 x^{3} y^{2} z^{3}

(option 3) is a polynomial.

4) x + x^{2} + x^{3} + x^{4}

It is an expression that uses just the addition operation and only one variable, x. The four exponents of the variable x are 1, 2, 3, and 4, and they are all positive integers.
Hence,