# Which one of the following is a polynomial

a. x²/2 - 2/x²

b. √2x - 1

c. x² + 3x^{3/2}/ √x

d. (x - 1)/ (x + 1)

**Solution:**

Let us simplify each option

a. x²/2 - 2/x²

= x²/2 - 2x^{-2}

As one of the exponents of x is -2 which is not a whole number, it is not a polynomial.

b. **√**2x - 1

= **√**2x^{1/2} - 1

As the exponent of x is 1/2 which is not a whole number, it is not a polynomial.

c. x² + 3x^{3/2}/ **√**x

= x² + 3x^{3/2 - ½}

= x² + 3x

As the exponent of x is the whole number, it is a polynomial.

d. (x - 1)/ (x + 1)

As it is a rational function, it is not a polynomial.

Therefore, x² + 3x^{3/2}/ **√**x is a polynomial.

**✦ Try This: **If x² + kx + 6 = (x + 7) (x + 8) for all x, then the value of k is

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 2

**NCERT Exemplar Class 9 Maths Exercise 2.1 Problem 1**

## Which one of the following is a polynomial? a. x²/2 - 2/x², b. √2x - 1, c. x² + 3x^{3/2}/ √x, d. (x - 1)/ (x + 1)

**Summary:**

A polynomial is a type of expression in which the exponents of all variables should be a whole number. x² + 3x^{3/2}/ √x is a polynomial

**☛ Related Questions:**

visual curriculum