# 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) $7 x^{3}$

#### Complete Python Prime Pack

9 Courses     2 eBooks

#### Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

#### Java Prime Pack

9 Courses     2 eBooks

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.

Updated on 10-Oct-2022 13:39:07