Classify the following as linear, quadratic and cubic polynomials:
(i) $ x^{2}+x $
(ii) $ x-x^{3} $
(iii) $ y+y^{2}+4 $
(iv) $ 1+x $
(v) $ 3 t $
(vi) $ r^{2} $
(vii) $ 7 x^{3} $

To do: 

We have to classify the given polynomials as linear, quadratic and cubic polynomials.

Solution: 

Polynomials are expressions in which each term is a constant multiplied by a variable raised to a whole number power.

A linear polynomial is a polynomial of degree 1.

A quadratic polynomial is a polynomial of degree 2.

A cubic polynomial is a polynomial of degree 3.

A polynomial's degree is the highest or the greatest power of a variable in a polynomial.

Therefore,

(i) In \( x^{2}+x \), the term $x^2$ has a variable of power $2$.

This implies, the degree of \( x^{2}+x \) is $2$.

Therefore, the given polynomial is a quadratic polynomial.     

 (ii) In \( x-x^{3} \), the term $-x^3$ has a variable of power $3$.

This implies, the degree of \( x-x^{3} \) is $3$.

Therefore, the given polynomial is a cubic polynomial.     

(iii) In \( y+y^{2}+4 \), the term $y^2$ has a variable of power $2$.

This implies, the degree of \( y+y^{2}+4 \) is $2$.

Therefore, the given polynomial is a quadratic polynomial.     

(iv) In \( 1+x \), the term $x$ has a variable of power $1$.

This implies, the degree of \( 1+x \) is $1$.

Therefore, the given polynomial is a linear polynomial.     

(v) In \( 3t \), the term $3t$ has a variable of power $1$.

This implies, the degree of \( 3t \) is $1$.

Therefore, the given polynomial is a linear polynomial.     

(vi) In \( r^{2} \), the term $r^2$ has a variable of power $2$.

This implies, the degree of \( r^{2} \) is $2$.

Therefore, the given polynomial is a quadratic polynomial.     

 (vii) In \( 7x^{3} \), the term $7x^3$ has a variable of power $3$.

This implies, the degree of \( 7x^{3} \) is $3$.

Therefore, the given polynomial is a cubic polynomial.