# Ex.2.1 Q5 Polynomials Solution - NCERT Maths Class 9

## Question

Classify the following as linear, quadratic and cubic polynomials:

(i) \(\begin{align}x^{2}+x\end{align}\)

(ii) \(\begin{align}x-x^{3}\end{align}\)

(iii) \(\begin{align}y+y^{2}+4\end{align}\)

(iv) \(\begin{align}1+x\end{align}\)

(v) \(\begin{align}3 t\end{align}\)

(vi) \(\begin{align}r^{2}\end{align}\)

(vii) \(\begin{align}7 x^{3}\end{align}\)

## Text Solution

**Reasoning:**

A polynomial of degree one is called a linear polynomial.

A polynomial of degree two is called a quadratic polynomial.

A polynomial of degree three is called a cubic polynomial.

**Steps:**

(i) \(\begin{align}x^{2}+x \rightarrow\end{align}\) Quadratic polynomial since the degree is \(2.\)

(ii) \(\begin{align}x-x^{3} \rightarrow\end{align}\) Cubic polynomial since the degree is \(3.\)

(iii) \(\begin{align}y+y^{2}+4 \rightarrow\end{align}\) Quadratic polynomial since the degree is \(2.\)

(iv)\(\begin{align}1+x \rightarrow\end{align}\) Linear polynomial since the degree is \(1.\)

(v) \(\begin{align}3 t \rightarrow\end{align}\) Liner polynomial since the degree is \(1.\)

(vi) \(\begin{align}r^{2} \rightarrow\end{align}\) Quadratic polynomial since the degree is \(2.\)

(vii) \(\begin{align}7 x^{3} \rightarrow\end{align}\) Cubic polynomial since the degree is \(3.\)