Which of the following expressions are polynomials? Find the number of variables of the polynomials:

i. 3x² – 5x + 13

ii. y² + 2√3

iii.

iv. 3

v. 2√x + √3x

vi. x¹² + y³ + t²⁰

A polynomial is an expression having numbers and letters or symbols.

Poly means many i.e. the expression can have many terms

The letters or symbols are called as variables

(i) 3x² – 5x + 13

yes 3x² – 5x + 13 is a polynomial

the letter here is ‘x’ so x is the only variable so the number of variables is 1

(ii) y² + 2√3

yes y² + 2√3 is a polynomial

the letter here is ‘y’ so y is the only variable so number of variables is 1

iii.

yes is a polynomial

the letter here is ‘y’ so y is the only variable so the number of variables is 1

iv. 3

yes 3 is also polynomial without any variable, hence the number of variables is 0 because 3 is a number a constant hence it is also called as a constant polynomial

v. 2√x + √3x

yes 2√x + √3x is a polynomial

the letter here is ‘x’ so x is the only variable so number of variables is 1

vi. x¹² + y³ + t²⁰

yes x¹² + y³ + t²⁰ is a polynomial

the letters here in this polynomial are x, y and t so there are 3 variables x, y and t