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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

Welcome to **nub****trek**.

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

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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.

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

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

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

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

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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

*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

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

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 '.