1.Which of the following expression are polynomials in one variable and which are not?

State reason for your answer.

i)\(4x^2 - 3x + 7\)

ii)\(y^2 + \sqrt{2}\)

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

iv)\(y + 2/y\)

v)\(x^{10} + y^3 + t^{50}\)

State reason for your answer.

i)\(4x^2 - 3x + 7\)

ii)\(y^2 + \sqrt{2}\)

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

iv)\(y + 2/y\)

v)\(x^{10} + y^3 + t^{50}\)

i) \(4x^2 - 3x + 7\) is a polynomail in one variable. As it is having only non-negative integral powers of x.

ii)\(y^2 + \sqrt{2}\) is also a polynomial in one variable. As it is having only non-negative integral power of y.

iii)\(3\sqrt{t} + t\sqrt{2}\) is not a polynomial. As the integral power of the variable is not a whole number.

iv)\(y + 2/y\) is not a polynomial. As it having a negative integral power of y.

v) \(x^{10} + y^3 + t^{50}\) is a polynomial with three variables.