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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.
mathsIntroduction to Algebra, Polynomials, and IdentitiesPolynomials - Basics

### Degree of Polynomials

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

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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 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
• 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
• 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?

• Pronunciation : Say the answer once
Spelling: Write the answer once

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
• 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
• 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
• 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
• 0
• 23

The answer is '0'. This can be called polynomial of degree 0, which is a "constant".

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

• vertically downwards
• along a 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'?

• a four sided figure
• related to square
• 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
• 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?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is 'linear polynomial'.

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

• Pronunciation : Say the answer once
Spelling: Write the answer once

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

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is 'cubic polynomial'.

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

• Pronunciation : Say the answer once
Spelling: Write the answer once

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.

Solved Exercise Problem:

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

• 6
• 5
• 3
• 3

The answer is '3'.

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