**Q.1.** Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(i) 4*x*^{2} - 3*x* + 7 (ii) *y*^{2} + $\sqrt{2}$ (iii) 3$\sqrt{\mathrm{t}}$ + *t*$\sqrt{2}$

(iv) *y* + $\frac{2}{\mathrm{y}}$ (v) *x*^{10} + *y*^{3} + *t*^{50}

**Solution:**

- 4
*x*^{2}- 3*x*+ 7: This is an expression with only one variable x with +ve integer powers. Hence, this is a polynomial in one variable. *y*^{2}+ $\sqrt{2}$: This is an expression with only one variable y with +ve integer powers. Hence, this is a polynomial in one variable.- 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. *y*+ $\frac{2}{\mathrm{y}}$ =*y*+ 2*y*^{-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.*x*^{10}+*y*^{3}+*t*^{50}:There are three variable*x*,*y*and*t*, hence, this is not a polynomial in one variable.