Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(i) 4x² - 3x + 7

(ii) y² + $\sqrt{2}$

(iii) $3\sqrt{t} + t\sqrt{2}$

(iv) $y + \dfrac{2}{y}$

(v) x¹⁰ + y³ + t⁵⁰

(i) 4x² - 3x + 7
It's a polynomial in one variable i.e., x

(ii) y² + $\sqrt{2}$
It's a polynomial in one variable i.e., y

(iii) $3\sqrt{t}$ + $t\sqrt{2}$ = 3t^1/2 + t $\sqrt{2}$
It is not a polynomial as degree of t is not a whole number.

(iv) y + $\dfrac{2}{y}$ = y + 2y^-1
It is in not a polynomial as degree cannot be negative (-ve) in polynomial.

(v) x¹⁰ + y³ + t⁵⁰
It is polynomial but not in one variable as variables are x, y and t here. Hence, it is a polynomial in three variables.