Question

Which of the following expressions are not polynomials?

(i) x² + 2x^-2

(ii) \(\sqrt{a}x\) + x² - x³

(iii) 3y³ - \(\sqrt{5}y\) + 9

(iv) ax^1/2 + ax + 9x² + 4

(v) 3x^-3 + 2x^-1 + 4x + 5

Answer 1

(i) x² + 2x^-2

A polynomial never has negative or fractional power. In the given expression x has negative power.

Therefore it is not a polynomial.

(ii)  \(\sqrt{a}x\) + x² - x³

A polynomial always has positive power.

Therefore the given expression is a polynomial.

(iii) 3y³ - \(\sqrt{5}y\) + 9

A polynomial always has positive power.

Therefore the given expression is a polynomial.

(iv) ax^1/2 + ax + 9x² + 4

A polynomial never has negative or fractional power. In the given expression x has fractional power.

Therefore it is not a polynomial.

(v) 3x^-3 + 2x^-1 + 4x + 5

A polynomial never has negative or fractional power. In the given expression x has negative power.

Therefore it is not a polynomial.