Question

Question 1
Which of the following expressions are polynomials in one variable and which are not?
(i) $4x^2-3x+7$
(ii) $y^2+\sqrt{2}$
(iii) $3\sqrt{t}+t\sqrt{2}$
(iv) $y+\frac{2}{y}$
(v) $x^{10}+y^3+t^{50}$

Answer 1

(i) Polynomial in one variable x.

(II) $4x^2-3x+7$
It is a polynomial in one variable, y.

(iii) $3\sqrt{t}+t\sqrt{2}$ is not a polynomial as power of t in $\sqrt{t}$ is not a whole number.

(iv) $y+\frac{2}{y}$ is not a polynomial as power of y in second term, i.e., $\frac{1}{y}=y^{-1}$ is not a whole number.

(v) $x^{10}+y^3+t^{50}$ is not a polynomial in one variable but a polynomial in three variables x, y and t.