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Thought-Process to Discover Knowledge

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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.

User Guide

Welcome to nubtrek.

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

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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.

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.

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.

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.

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.

summary of this topic

### Polynomial Arithmetics

Voice

Voice

Home

Simplification of Polynomials

»  numbers in different forms
→  simplified form of 7-2/2 is 6
→  prime factorization of 6 is 3 xx 2

»  Polynomials are simplified to General form: sum of irreducible terms
irreducible terms are terms that cannot be equivalently given as multiple simpler terms.
→  eg: x^3-x^2-4x+4

»  Polynomials in factors form: product of irreducible factors.
→  eg: (x-1)(x-2)(x+2)

### Simplification of Polynomials

plain and simple summary

nub

plain and simple summary

nub

dummy

polynomial simplification can be in one of the two forms

•  general form of polynomial

•  factors form of polynomial

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Polynomials can be equivalently represented in different forms. The simplified polynomial form is given as sum of terms that are reduced to multiplication of variables. The factors form is given as product of factors that are reduced to the smallest factors.

Keep tapping on the content to continue learning.
Starting on learning "Simplification of Polynomials". ;; Polynomials can be equivalently represented in different forms. The simplified polynomial form is given as sum of terms that are reduced to multiplication of variables. The factors form is given as product of factors that are reduced to the smallest factors.

Which of the following equals 6?

• 6
• 3+2(4-2)-1
• 3xx2
• all the above

The answer is 'all the above'

All the following represent the same quantity.

» 6 : simplified form

» 3+2(4-2)-1

» 3xx2 : prime factors form

A numerical expression may be evaluated to a number and that is "simplified form"

A number may be represented as product of prime factors and that is "prime factors form"

Which of the following equals x^2+x(x+4)-30?

• 2x^2+4x-30
• 12x^2-x^2(7+3) -26+4x-2^2
• (2x-6)(x+5)
• all these are equal

The answer is 'all these are equal'

An expression can be represented in multiple forms.

»  x^2+x(x+4)-30

»  2x^2+4x-30

»  12x^2-x^2(7+3) -26+4x-2^2

»  (2x-6)(x+5)

In these, two forms are simplified.

»  2x^2+4x-30 : Simplified Polynomial in general form which is given as addition or subtraction of irreducible terms.

»  (2x-6)(x+5) : Polynomial in factors form, which is given as product of irreducible factors.

Given polynomial x^2+ x(x+2)-23, What is the part x(x+2) called?

• a term
• a sub-expression

The answer is 'a sub-expression'. x(x+2) is not a term as it can be given as x^2+2x which has two terms.

The given polynomial x^2 + x(x+2)-23 can be equivalently given as follows.

x^2 + x(x+2)-23
=x^2 + x^2+2x-23
=2x^2 +2x-23

The derived polynomial 2x^2 +2x-23 is simpler and has terms that cannot be reduced further. This polynomial has irreducible terms.

Given polynomial (x-1)(x^2-4), What is the part (x-1) called?

• a factor
• a term

The given polynomial (x-1)(x^2-4)can be equivalently given as follows.

(x-1)(x^2-4)
=(x-1)(x-2)(x+2)

The derived polynomial (x-1)(x-2)(x+2) is simpler and has factors that cannot be factorized further. This polynomial form is in irreducible factors.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Polynomial Simplification: A polynomial can be simplified to

•  general form: sum of terms reduced to exponent of variables without any addition or subtraction.

•  factors form: product of polynomials factorized to irreducible factors.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Express (x+2)(2x-2) in general form of polynomial.

• 2x^2+2x-4
• x+4x-2
• 5x-2

The answer is '2x^2+2x-4'

Progress

Progress

Which of the following equals 6 ?
6
6
plus;minus
3 plus 2 times 4 minus 2, minus 1
multiplied
3 multiplied 2
all;above
all the above
The answer is 'all the above'
All the following represent the same quantity. 6 : simplified form. 3 plus 2 times 4 minus 2 minus 1. ;; 3 multiplied 2 : prime factors form. ;; A numerical expression may be evaluated to a number and that is "simplified form". ;; A number may be represented as product of prime factors and that is "prime factors form"
Which of the following equals x squared + x multiplied x + 4 minus 30.
1
2
3
4
The answer is 'all these are equal'
An expression can be represented in multiple forms. In these two forms are simplified.;; 2 x squared + 4 x minus 30: simplified polynomial in general form which is given as addition or subtraction of irreducible terms. ;; 2x minus 6 multiplied x + 5 : Simplified Polynomial in factors form, which is given as product of irreducible factors.
Given polynomial, what is the part x multiplied x + 2 called?
term
a term
sub;expression;express
a sub-expression
The answer is "a sub-expression". x multiplies x+2 is not a term as it can be given as x squared + 2 x which has two terms.
The given polynomial can be equivalently reduced. ;; The derived polynomial 2 x squared + 2 x minus 23 is simpler and has terms that cannot be reduced further. This polynomial has irreducible terms.
Given polynomial, what is the part x minus 1 called?
factor
a factor
term
a term