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summary of this topic

### 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

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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?

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?

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

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

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

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'.

Progress

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
What is the word or phrase used to refer a polynomial of degree 2 ?
What is the word or phrase used to refer a polynomial of degree 3 ?
cubic
What is the word or phrase used to refer a polynomial of degree 0 ?
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 '.

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