Q.1. 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$\sqrt{\mathrm{t}}$ + t$\sqrt{2}$

(iv) y + $\frac{2}{\mathrm{y}}$ (v) x10 + y3 + t50

Solution:

1. 4x2 - 3x + 7: This is an expression with only one variable x with +ve integer powers. Hence, this is a polynomial in one variable.

2. y2 + $\sqrt{2}$: This is an expression with only one variable y with +ve integer powers. Hence, this is a polynomial in one variable.

3. 3$\sqrt{\mathrm{t}}$ + t$\sqrt{2}$: This is an expression with only one variable t but one of the powers of t is $\frac{1}{2}$ (in 3$\sqrt{\mathrm{t}}$), which is not +ve integer. Hence, this is not a polynomial.

4. y + $\frac{2}{\mathrm{y}}$ = y + 2y-1: This is an expression with only one variable y but one of the powers of y is -1, which is not +ve integer. Hence, this is not a polynomial.

5. x10 + y3 + t50:There are three variable x, y and t, hence, this is not a polynomial in one variable.