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# 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.

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