Server Not Reachable. *This may be due to your internet connection or the nubtrek server is offline.*

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

Voice

Voice

Home

» **like terms** : Terms that have identical variables with identical exponents of those variables

» **unlike terms** : Terms that differ in the variables or in the exponents of those variables

» **Classification of Polynomials Based on terms**:*the like terms are combined.*

→ **monomial** : one term

→ **binomial** : two terms

→ **trinomial** : three terms

→ **polynomial of n terms**

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

Like terms have same variables with same exponents.

Unlike terms differ in the variables or in the exponents.

Based on the number of terms in a polynomial the polynomials are classified as monomials, binomials, trinomials, and polynomials of `n` terms

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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 number of terms in a polynomial, the polynomial is classified as monomial, binomial, etc.

Starting on learning "Terms of Polynomials". ;; Based on the number of terms in a polynomial, the polynomial is classified as monomial, binomial, et cetera.

What is the word or phrase used to refer to parts of a polynomial consist of product of numbers and variables?

- a term
- a coefficient

The answer is 'a term'.

What is the word used to refer the number part in a term?

- a term
- a coefficient

The answer is 'a coefficient'.

How many terms are there in the polynomial `3x^2y^5`?

- `1`
- `2`
- `3`

The answer is '`1`'. This is an example of *polynomial with one term, called "monomial"*.

How many terms are there in the polynomial `3x^2 + y^5`?

- `1`
- `2`
- `3`

The answer is '`2`'. This is an example of *polynomial with two terms, called "binomial"*

How many terms are there in the polynomial `x^2y+y^2z+xz^2`?

- `1`
- `2`
- `3`

The answer is '`3`'. This is an example of *polynomial with 3 terms, called "trinomial"*

Based on the number of terms in a polynomial the polynomials are classified as

• monomial

• binomial

• trinomial

• polynomial of n terms

Is `(2x^2+x^2)` a polynomial?

- yes
- no

The answer is 'Yes'.

Is `3x^2` a polynomial?

- yes
- no

The answer is 'Yes'.

Consider the polynomials

• `(2x^2+x^2)`

• `3x^2`

Remember that the polynomials represent quantities. If `x` is a number and takes value `2`, the two polynomials

`(2x^2+x^2) = 2 xx 2^2 + 2^2 = 12`

`3 xx 2^2 = 3 xx 4 = 12`

Both of these two polynomials evaluate to identical values for all values of `x`.

Consider the polynomials

• `(2x^2+x^2)`

• `3x^2`

These polynomials are equal for all values of `x`. This is explained with the following.

`2 x^2 + x^2`*substitute multiplying by 2 as repeated addition.*

` = x^2 + x^2 + x^2`*count the repeated addition and convert to multiply by the number *

` = 3 x^2`

This is the second polynomial.

The above is generalized as distributive property of multiplication over addition. This part will be explained in "number system or algebra in high school".

For now, we can understand that two terms having same variable combination, the coefficients can be combined to form a single term.

Example: `2.3x^5y^7 + 1.1x^5y^7`

`quad = (2.3+1.1) x^5y^7`

`quad = 3.4x^5y^7`

Terms that differ only in the coefficient part can be combined. Such terms are called "like terms".

Terms that differ in variables or exponents of variables are called "unlike terms".

Are `2x^3y^2` and `(x^3y^2)/7` like or unlike terms?

- like terms
- unlike terms

The answer is 'like terms'. The difference is in the coefficients `2` and `1/7`.

Are `2x^2y` and `(x^2z)/7` like or unlike terms?

- like terms
- unlike terms

The answer is 'unlike terms'. The terms differ in the variables.

Are `2xy^2` and `3.1(xy)^2` like or unlike terms?

- like terms
- unlike terms

The answer is 'unlike terms'. The terms differ in the exponents of variables.

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

- a large water body
- having same characteristics or qualities

The answer is 'having same characteristics or qualities'.

What is two terms having identical variables with identical exponents called?

- Practice Saying the Answer

The answer is 'like terms'.

What does the word 'unlike' mean?

- having different characteristics or qualities
- to remove water from a lake

The answer is 'having different characteristics or qualities'.

What is two terms having different variables or different exponents called?

- Practice Saying the Answer

The answer is 'unlike terms'.

What type is the polynomial `(2x^2+x^2)` based on the number of terms?

- monomial
- binomial
- trinomial

The answer is 'monomial'. The like terms can be combined and so the polynomial is a monomial.

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

- one term
- control over something

The answer is 'one term'. *monomial means "one"(mono) + "term"(nomial)*.

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

- five terms
- two terms

The answer is '2 terms'. *binomial means "two"(bi) + "term"(nomial).*

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

- three sides
- three terms

The answer is 'three terms'. *trinomial means "three"(tri) + "term"(nomial).*

What is the term used to refer polynomial of 1 term ?

- Practice Saying the Answer

The answer is 'monomial'.

What is the term used to refer polynomial of 2 terms ?

- Practice Saying the Answer

The answer is 'binomial'.

What is the term used to refer polynomial of 3 terms ?

- Practice Saying the Answer

The answer is 'trinomial'.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Like Terms: ** The terms that has identical variables with identical exponents are called like terms. **Unlike Terms: ** The terms that differ in the variables or in the exponents of the variables are called unlike terms.

**Classification of polynomials based on the number of terms: ** After combining any like terms in polynomials, the number of terms is considered. Polynomials are classified as

• monomial

• binomial

• trinomial

• polynomial of `n` terms

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

What type is the polynomial `(x^4+2xy^2+xy^2-x^4)` based on the number of terms?

- monomial
- binomial
- trinomial

The answer is 'monomial'. The like terms can be combined and two terms combine to `0`. So, the polynomial is a monomial.

*your progress details*

Progress

*About you*

Progress

What is the word or phrase used to refer to parts of a polynomial consist of product of numbers and variables?

term

a term

coefficient

a coefficient

The answer is 'a term'.

What is the word used to refer the number part in a term?

term

a term

coefficient

a coefficient

The answer is 'a coefficient'.

How many terms are there in the given polynomial?

1

1

2

2

3

3

The answer is ' 1 '. This is an example of polynomial with one term, called "monomial".

How many terms are there in the given polynomial?

1

1

2

2

3

3

The answer is ' 2 '. This is an example of polynomial with two terms, called "binomial"

How many terms are there in the given polynomial?

1

1

2

2

3

3

The answer is ' 3 '. This is an example of polynomial with 3 terms, called "trinomial"

Based on the number of terms in a polynomial, the polynomials are classified as monomial, binomial, trinomial, and polynomial of n terms.

Is 2 x squared + x power 2 a polynomial?

yes;s

yes

no

no

The answer is 'Yes'.

Is 3 x squared a polynomial?

yes;s

yes

no

no

The answer is 'Yes'.

Consider the polynomials. ;; Both of these two polynomials evaluate to identical values for all values of x.

Consider the polynomials 2 x squared + x squared and 3 x squared. These polynomials are equal for all values of x. This is explained with the following.

The above is generalized as distributive property of multiplication over addition. This part will be explained in "number system or algebra in high school". ;; For now, we can understand that two terms having same variable combination, the coefficients can be combined to form a single term.

Terms that differ only in the coefficient part can be combined. Such terms are called "like terms". ;; Terms that differ in variables or exponents of variables are called "unlike terms".

Are these two terms like or unlike terms?

like

like terms

unlike

unlike terms

The answer is 'like terms'. The difference is in the coefficients 2 and 1 by 7.

Are these two terms like or unlike terms?

like

like terms

unlike

unlike terms

The answer is 'unlike terms'. The terms differ in the variables.

Are these two terms like or unlike terms?

like

like terms

unlike

unlike terms

The answer is 'unlike terms'. The terms differ in the exponents of variables.

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

large;water;body

a large water body

having;same;characteristics;qualities

having same characteristics or qualities

The answer is 'having same characteristics or qualities'.

What is two terms having identical variables with identical exponents called?

like

The answer is 'like terms'.

What does the word 'unlike' mean?

different;characteristics;qualities

having different characteristics or qualities

remove;water;from

to remove water from a lake

The answer is 'having different characteristics or qualities'.

What is two terms having different variables or different exponents called?

unlike

The answer is 'unlike terms'.

Like terms have same variables with same exponents.;; Unlike terms differ in the variables or in the exponents.

Like Terms: The terms that has identical variables with identical exponents are called like terms. ;; unlike terms: the terms that differ in the variables or int he exponents of the variables are called unlike terms.

What type is the polynomial 2 x squared + x squared, based on the number of terms?

monomial

monomial

binomial

binomial

trinomial

trinomial

The answer is 'monomial'. The like terms can be combined and so the polynomial is a monomial.

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

1;term

one term

control;over

control over something

The answer is 'one term'. monomial means one + term.

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

5

five terms

2

two terms

The answer is '2 terms'. binomial means two + term.

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

sides

three sides

terms

three terms

The answer is 'three terms'. *trinomial means "three"(tri) + "term"(nomial).*

What is the term used to refer polynomial of 1 term ?

monomial

The answer is 'monomial'.

What is the term used to refer polynomial of 2 terms ?

binomial

The answer is 'binomial'.

What is the term used to refer polynomial of 3 terms ?

trinomial

The answer is 'trinomial'.

Based on the number of terms in a polynomial the polynomials are classified as monomials, binomials, trinomials, and polynomials of n terms

Classification of polynomials based on the number of terms: After combining any like terms in polynomials, the number of terms is considered. Polynomials are classified as monomial, binomial, trinomial, polynomial of n terms.

What type is the given polynomial based on the number of terms?

monomial

monomial

binomial

binomial

trinomial

trinomial

The answer is 'monomial'. The like terms can be combined and two terms combine to 0 . So, the polynomial is a monomial.