nubtrek

Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

User Guide   

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
  think,
  figure-out, &
  learn.

Just keep tapping (or clicking) on the content to continue in the trail and learn. continue

User Guide   

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

  nub,

  trek,

  jogger,

  exercise.

continue

User Guide    

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

User Guide    

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

User Guide    

jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen. continue

User Guide    

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

summary of this topic

Polynomials - Basics

Polynomials - Basics

Voice  

Voice  



Home




 »  Classification of Polynomial Based on degree:
    →  linear polynomial of degree 1
    →  quadratic polynomial of degree 2
    →  cubic polynomial of degree 3
    →  polynomial of degree n


 »  Degree of a polynomial : The highest sum of power of variable among the terms of polynomial.
    →  eg: Degree of polynomial `2x^2y^2+x^3+2^7y^2` is `4`
    →  degree of first term `x^2y^2` is `2+2=4`, that is sum of powers
    →  degree of second term `x^3` is `3`.
    →  degree of third term `2^7y^2` is `2`, as the power of variables

Degree of Polynomials

plain and simple summary

nub

plain and simple summary

nub

dummy

Degree of a polynomial is the highest exponent value with all variables combined.

Based on the degree of a polynomial, they are classified as constant, linear, quadratic, cubic, and polynomial of degree `n`.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

Support Nubtrek     
 

You are learning the free content, however do shake hands with a coffee to show appreciation.
To stop this message from appearing, please choose an option and make a payment.




Based on the highest value of sum of exponents of terms, polynomials are classified as linear, quadratic, cubic, etc.


Keep tapping on the content to continue learning.
Starting on learning about "Degree of polynomials". ;; Based on the highest value of sum of exponents of terms, polynomials are classified as linear, quadratic, cubic, et cetera.

What is the similarity between the given polynomials of single variable?

`x^2+3`
`sqrt(5)x^2-8x-2`
`4x^2+8x`
`-2x^2`

  • no similarity is found
  • the highest power or exponent of the variable is `2`

The answer is 'the highest power or exponent of the variable is `2`'

When the highest power is equal, a generic form can be derived. For example, `ax^2+bx+c` is the generic form for all the following polynomials.


`ax^2+bx+c` (given generic form)

`x^2+3` (`a=1; b=0; c=3`)

`sqrt(5)x^2-8x-2` (`a=sqrt(5); b=-8; c=-2 `)

`4x^2+8x` (`a=4; b=8; c=0`)

`-2x^2` (`a=-2; b=0; c=0`)

What is the highest power of `x^3y^2+xy^2+x^4+3`?

  • `3`
  • `4`
  • `5`
  • maximum power is not defined for polynomial of two variables

The answer is '`5`'. The term `x^3y^2` is the one with the highest power of variables. The highest power is `3+2 = 5`.

The highest sum of powers of variables in a term is called degree of the polynomial.

Which of the following is a meaning for the word 'degree'?

  • amount or level at which something is present
  • rotation in clockwise direction

The answer is 'amount or level at which something is present'. The degree of a polynomial is the highest power of the variables in the terms.

What is the word or phrase used to refer the highest power of the variables in a polynomial?

  • Practice Saying the Answer

The answer is 'degree of the polynomial'.

What is the degree of the polynomial `23 x+2`?

  • `1`
  • `2`
  • `23`

The answer is '`1`'. This is an example of polynomial of degree 1, also called "linear polynomial".

what is the degree of the polynomial `3x^2+3x+3`?

  • `1`
  • `2`
  • `3`

The answer is '`2`'. This is an example of polynomial of degree 2, also called "quadratic polynomial".

what is the degree of the polynomial ` xy^2+2xyz+yz`?

  • `1`
  • `2`
  • `3`

The answer is '`3`'. This is an example of polynomial of degree 3, also called "cubic polynomial".

What is the degree of the polynomial `23`?

  • `1`
  • `0`
  • `23`

The answer is '`0`'. This is an example of polynomial of degree 0, also called "constant".

Which of the following is a meaning for the word 'linear'?

  • vertically downwards
  • along a straight line

The answer is 'along a straight line'. The graph of a linear polynomial is a straight line.

Which of the following is a meaning for the word 'quadratic'?

  • a four sided figure
  • related to square

The answer is 'related to square'. The square is in two dimensions and degree of quadratic polynomials is `2`. The word "quadri" is used to denote `4` as a square is of four sides.

Which of the following is a meaning for the word 'cubic'?

  • related to 3D shape cube
  • a personal cell or room

The answer is 'related to 3D shape cube'. The cube is in 3 dimensions and degree of cubic polynomial is `3`.

What is the word or phrase used to refer a polynomial of degree `1`?

  • Practice Saying the Answer

The answer is 'linear polynomial'.

What is the word or phrase used to refer a polynomial of degree `2`?

  • Practice Saying the Answer

The answer is 'quadratic polynomial'.

What is the word or phrase used to refer a polynomial of degree `3`?

  • Practice Saying the Answer

The answer is 'cubic polynomial'.

What is the word or phrase used to refer a polynomial of degree `0`?

  • Practice Saying the Answer

The answer is 'constant'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Degree of a Polynomial : In a polynomial of multiple variables, for each of the terms, the sum of exponents of all variables is compared and the highest sum is the degree of the polynomial.

Classification of Polynomial based on degree of polynomial :

 • constant : polynomial of degree `0`.

 • linear : polynomial of degree `1`.

 • quadratic : polynomial of degree `2`.

 •  cubic : polynomial of degree `3`.

 •  polynomial of degree `n`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

what is the degree of the polynomial `3x^2y+3xy^2+3z^2`?

  • `6`
  • `5`
  • `3`

The answer is '`3`'.

your progress details

Progress

About you

Progress

What is the similarity between the given polynomials of single variable?
no;similarity;found
no similarity is found
highest;power;exponent;variable;2
the highest power or exponent of the variable is 2
The answer is 'the highest power or exponent of the variable is 2 '
When the highest power is equal, a generic form can be derived. For example, a x squared + b x + c is the generic form for all the following polynomials.
What is the highest power of the given polynomial?
3
3
4
4
5
5
maximum;power;defined;not
maximum power is not defined for polynomial of two variables
The answer is "5". The term x power 3 multiplied y power 2 is the one with the highest power of variables. The highest power is 3 plus 2 equals 5.
The highest sum of powers of variables in a term is called degree of the polynomial.
Which of the following is a meaning for the word 'degree'?
amount;level;something;present;at
amount or level at which something is present
rotation;clockwise;direction
rotation in clockwise direction
The answer is 'amount or level at which something is present'. The degree of a polynomial is the highest power of the variables in the terms.
What is the word or phrase used to refer the highest power of the variables in a polynomial?
degree
The answer is 'degree of the polynomial'.
degree of a polynomial is the highest exponent value with all variables combined.
Degree of a Polynomial : In a polynomial of multiple variables, for each of the terms, the sum of exponents of all variables is compared, and the highest sum is the degree of the polynomial.
What is the degree of the polynomial 23 x+2 ?
1
1
2
2
23
23
The answer is ' 1 '. This is an example of polynomial of degree 1, also called "linear polynomial".
What is the degree of the given polynomial?
1
1
2
2
3
3
The answer is ' 2 '. This is an example of polynomial of degree 2, also called "quadratic polynomial".
What is the degree of the given polynomial?
1
1
2
2
3
3
The answer is ' 3 '. This is an example of polynomial of degree 3, also called "cubic polynomial".
What is the degree of the polynomial 23 ?
1
1
0
0
23
23
The answer is ' 0 '. This is an example of polynomial of degree 0, also called "constant".
Which of the following is a meaning for the word 'linear'?
vertically;downwards
vertically downwards
along;straight;line
along a straight line
The answer is 'along a straight line'. The graph of a linear polynomial is a straight line.
Which of the following is a meaning for the word 'quadratic'?
4;sided;figure
a four sided figure
related;2;to;square
related to square
The answer is 'related to square'. The square is in two dimensions and degree of quadratic polynomials is of degree 2 . The word "quadri" is used to denote 4 as a square is of four sides.
Which of the following is a meaning for the word 'cubic'?
related;2;3;shape;cube
related to 3D shape cube
personal;cell;room
a personal cell or room
The answer is 'related to 3D shape cube'. The cube is in 3 dimensions and degree of cubic polynomial is 3 .
What is the word or phrase used to refer a polynomial of degree 1 ?
linear
The answer is 'linear polynomial'.
What is the word or phrase used to refer a polynomial of degree 2 ?
quadratic
The answer is 'quadratic polynomial'.
What is the word or phrase used to refer a polynomial of degree 3 ?
cubic
The answer is 'cubic polynomial'.
What is the word or phrase used to refer a polynomial of degree 0 ?
constant
The answer is 'constant'.
Based on the degree of a polynomial, they are classified as constant, linear, quadratic, cubic, and polynomial of degree n
Classification of polynomial based on degree of polynomial: ;; constant: polynomial of degree 0. ;;linear : polynomial of degree 1. ;; quadratic : polynomial of degree 2. ;; cubic : polynomial of degree 3. ;; polynomial of degree n.
what is the degree of the given polynomial?
6
6
5
5
3
3
The answer is ' 3 '.

we are not perfect yet...

Help us improve