# Ex.2.1 Q1 Polynomials Solution - NCERT Maths Class 9

## Question

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

(i) \(\begin{align}4 x^{2}-3 x+7\end{align}\)

(ii) \(\begin{align}y^{2}+\sqrt{2}\end{align}\)

(iii) \(\begin{align}3 \sqrt{t}+t \sqrt{2}\end{align}\)

(iv)\(\begin{align} y+\frac{2}{y}\end{align}\)

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

## Text Solution

**Steps :**

(i) \(\begin{align}4 x^{2}-3 x+7 \rightarrow\end{align}\) Polynomial in one variable \(x.\)

(ii) \(\begin{align}y^{2}+\sqrt{2} \rightarrow\end{align}\) Polynomial in one variable \(y.\)

(iii) \(\begin{align}3 \sqrt{t}+t \sqrt{2} \rightarrow\end{align}\) Not a polynomial, since the power of the variable in the first term is \(\begin{align}\frac{1}{2}\end{align}\) which is not a whole number.

(iv) \(\begin{align}y+\frac{2}{y} \rightarrow \end{align}\) Not a polynomial since the power of the variable in the second term is \(– 1\) which is not a whole number.

(v) \(\begin{align}x^{10}+y^{3}+t^{50} \rightarrow \end{align}\) Not a polynomial in one variable since there are \(3\) variables \(x, y, t.\)