Which of the following expressions are not polynomials?(i) x2 + 2x-2(i

1.	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) ax1/2 + ax + 9x2 + 4(v) 3x-3 + 2x-1 + 4x + 5
Answer» (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.

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) ax1/2 + ax + 9x2 + 4(v) 3x-3 + 2x-1 + 4x + 5

Answer»

(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.