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summary of this topic

Polynomials - Basics

Polynomials - Basics

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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

Terms of Polynomials

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

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


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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.

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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.

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