State whether the following expressions are polynomials in one variable or not. Give reasons for your answer.

i. 2x⁵ – x³ + x – 6

ii. 3x² – 2x + 1

iii. y³ + 2√3

iv.

v.

vi. x³ + y³ + z⁶

i. 2x⁵ – x³ + x – 6

There is only one variable ‘x’ with whole number power. So, this is polynomial in one variable.

ii. 3x² – 2x + 1

There is only one variable ‘x’ with whole number power. So, this is polynomial in one variable.

iii. y³ + 2√3

There is only one variable ‘y’ with whole number power. So, this is polynomial in one variable.

iv.

⇒

There is only one variable ‘x’ with whole number power. So, this is polynomial in one variable.

v. 3√ t + 2t

There is only one variable ‘t’ but in 3√t, power of t is which is not a whole number. So, this is not a polynomial in one variable.

vi. x³ + y³ + z³

There are three variables x, y and z, but power is whole number. So, this is not a polynomial in one variable.