FACTORING USING COMMON MONOMIAL FACTOR || GRADE 8 MATHEMATICS Q1

Summary

In this video, Monica explains how to find the greatest common factor (GCF) of numbers and polynomials using methods like listing and prime factorization. She covers the definition and examples of monomials, polynomials, and the process of factoring polynomials using the distributive property. Through detailed examples, Monica demonstrates step-by-step procedures to determine the GCF and factor polynomials completely. The video aims to enhance understanding of these mathematical concepts, making it easier for viewers to solve related problems.

Takeaways

• 📘 Understanding how to find the Greatest Common Factor (GCF) of polynomials.
• 📊 Two methods to find the GCF: Listing factors and Prime Factorization.
• 🔢 Explanation of monomials and polynomials, including their components like constants and variables.
• 🧩 Importance of arranging polynomials in standard form for easier factoring.
• 🧮 Definition of GCF: The greatest numerical factor with variables having the least degree.
• 🔍 Step-by-step example of finding GCF by listing factors and using prime factorization.
• 📐 Factoring pairs of monomials using prime factorization to identify common factors.
• 🔗 Applying the distributive property to factor polynomials using the GCF.
• 📈 Detailed examples of factoring various polynomials using GCF and distributive property.
• 📝 Rewriting polynomials as products of smaller degree polynomials for simpler solutions.

Q & A

What is the greatest common factor (GCF)?

The greatest common factor (GCF) is the largest number that divides two or more numbers without leaving a remainder.

How can we find the GCF by listing factors?

To find the GCF by listing factors, list all the factors of each number, then identify the largest factor that appears in each list.

What is prime factorization?

Prime factorization involves breaking down a number into its prime factors, which are prime numbers that multiply together to give the original number.

How do we use prime factorization to find the GCF?

To use prime factorization to find the GCF, break down each number into its prime factors, then identify the common prime factors and multiply them together.

What is a monomial?

A monomial is a type of polynomial that has only one term, which can be a constant, a variable, or the product of constants and variables.

How do we factor polynomials using the GCF?

To factor polynomials using the GCF, first find the GCF of all the terms in the polynomial, then divide each term by the GCF and write the polynomial as the product of the GCF and the resulting polynomial.

What is the standard form of a polynomial?

The standard form of a polynomial is when its terms are arranged in descending order of their degrees, from highest to lowest.

How do you determine the GCF of monomials with variables?

To determine the GCF of monomials with variables, find the GCF of the numerical coefficients and the lowest power of each common variable.

What is the distributive property?

The distributive property states that a(b + c) = ab + ac, which allows us to factor out a common factor from a polynomial.

How do you use the distributive property to factor polynomials?

To use the distributive property to factor polynomials, find the GCF of the terms, factor it out, and write the polynomial as the product of the GCF and the remaining polynomial.

Outlines

00:00

🎶 Introduction to Greatest Common Factor

In this video, Monica discusses the concept of the Greatest Common Factor (GCF) and its importance in mathematics. The GCF can be found through listing factors or prime factorization. The video will also cover polynomial factorization using the distributive property.

05:01

🔢 Finding the GCF with Examples

This section provides examples of finding the GCF of different pairs of monomials. It explains the process of using prime factorization to identify common factors and how to apply them in solving problems. The examples include pairs like 6a and 18aB, 10a and 12a²B, and negative 8x²y and 16xy.

10:03

✏️ Factoring Polynomials Using GCF

Monica explains how to factor polynomials by rewriting them as a product of polynomials of smaller degrees using the GCF. Examples include factoring 4x² + 6x and 3x² + 6x. The process of using the distributive property to simplify polynomials is detailed.

15:06

📐 Advanced Polynomial Factorization

This segment covers more complex examples of polynomial factorization. Monica demonstrates factoring expressions with multiple terms and different structures, such as 7/8a + 3 - c(a + 3) and combining like terms to simplify the factorization process.

Keywords

💡Greatest Common Factor (GCF)

The GCF is the highest number that divides two or more numbers without leaving a remainder. In the video, the GCF is found either by listing the factors of the numbers or by using prime factorization. For example, the GCF of 6x^2 and 15x^4 is found to be 3x^2.

💡Prime Factorization

Prime factorization involves breaking down a number into its basic prime number multipliers. This concept is used in the video to determine the GCF of given terms. For instance, 6 is broken down into 2 and 3, which are prime numbers.

💡Polynomial

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents combined using addition, subtraction, and multiplication. The video discusses factoring polynomials completely by finding the common monomial factor and using the distributive property.

💡Monomial

A monomial is a single term polynomial, consisting of a constant, a variable, or a product of constants and variables. For example, '6a' and '18aB' are monomials discussed in the video while finding their GCF.

💡Standard Form

Standard form refers to the way a polynomial is arranged in descending order of the degree of its terms. The video explains the importance of arranging polynomials in standard form to simplify the process of finding the GCF.

💡Common Monomial Factor

The common monomial factor is the highest common factor of the terms in a polynomial. The video demonstrates how to factor polynomials by identifying and factoring out the common monomial factor, such as 2x in the expression 4x^2 + 6x.

💡Distributive Property

The distributive property is a fundamental algebraic property used to multiply a single term and two or more terms inside a parenthesis. The video uses this property to rewrite polynomials in their factored form, making it easier to simplify and solve them.

💡Variable

A variable is a symbol used to represent an unknown number in mathematical expressions and equations. In the video, variables like x and y are used in polynomials to illustrate how to find the GCF and factor expressions.

💡Exponent

An exponent indicates how many times a number (the base) is multiplied by itself. The video discusses how to handle exponents while finding the GCF of terms like 6x^2 and 15x^4, where the exponent determines the power of the variable.

💡Factoring

Factoring is the process of breaking down a polynomial into simpler polynomials that, when multiplied together, give the original polynomial. The video teaches how to factor polynomials by identifying the GCF and using the distributive property.

Highlights

Introduction to the concept of the Greatest Common Factor (GCF).

Explanation of how to find the GCF by listing factors and using prime factorization.

Definition and examples of monomials and polynomials.

Description of standard form for polynomials and arranging them in descending order.

Detailed process of finding the GCF of given terms using listing and prime factorization.

Example of finding the GCF of 6x^2 and 15x^4 by listing factors.

Step-by-step explanation of finding the GCF using prime factorization for 6x^2 and 15x^4.

Examples of finding the GCF for pairs of monomials, such as 6a and 18aB.

Explanation of factoring polynomials completely using the GCF.

Example of factoring a polynomial 4x^2 + 6x using the GCF.

Discussion of another method to factor polynomials by dividing by the GCF.

Example of factoring 3x^2 + 6x using the GCF and verifying by multiplication.

Explanation of how to factor more complex polynomials like 6x^4 - 14x^2.

Introduction to factoring expressions with multiple terms using the GCF.

Example of factoring an expression like 7a(a + 3) - c(a + 3) by identifying the common factor.

Final example of factoring a complex polynomial involving multiple terms and common factors.

Encouragement to practice and apply these factoring techniques.

Transcripts

[Music]

hi Monica wama in this video that allaha

is not in how are we going to find the

greatest common factor or unity natal

what naughty GCF of course by listing or

prime factorization pagalava

we will factor polynomials completely

with common monomial factor and use

distributive property to factor

polynomials so before we proceed to the

discussion let us unlock first greatest

common factor or unity natal what

nothing GCF anima bang GCF and GCL at

the human factors Nahum one then semana

terms take note Kotaku muha dire no

common factors nila okuni not in your

penis Amata s kya from the word itself

greatest

sakuni not in your penis amitis no

factor nila panel aa prime factors

vaccine I've been adding prime factors

these are numbers at Ala Moana numbers

and banging factor in Geelong I won and

the number itself

halimbawa to so on factors Nonya i 1 and

itself three and five those are some of

the examples next monomial packs in a

benedict monomial this is a special kind

of polynomial nahusa and and in London

termini I turns yeah I is a LAN so from

the prefix mono means one so they we

only have one term for it and then

polynomial this is an expression

combined with constant

Etrigan phoenix AMISOM on constant

variable or weathering product of two

product non constant or variable or

product non constant and variable now

take note that part an exponent yeah

must be a whole number so hindi chaya

pointing Macarena negative exponent done

fraction or you may symbols next

standard form when we see standard form

this is a kind of arrangement of a

polynomial in descending order

paksy nominating descending order next

is simulations our highest degree to

list degree in Pina fam'ly Baba

okay greatest common factor it refers

the common factor having the greatest

numerical factor and with variables

having the least degree so on Kahuna net

in a numerical factor Alpena Jimenez

adds a variable name and patent and

including adding a young Pina from Ababa

and degree or exponent example marina

from 6x squared + 15 X raise to 4 so

panel not in Conan and GCF neato so by

listing pate not in Tonga win so I'm

gonna factor c6i 1 2 3 6 + x squared so

15 demand Marin time 1 3 5 15 + X raise

to 4 so panel not including and GCF I

know you common factor in along the

lower that is 3 take note the patent

greatest and then subpoenas Kohanim

variable Kahuna not a new Pina Chama

Baba and degree since Marin Tod tombola

1x okuni not a new pin hama baba and

degree and that is x squared so

therefore we will have 3x squared next

another way is by prime factorization so

6x squared so Miggy Zipkin among of

factors num number or terminal now prime

number long so halimbawa high six so

Hindi moon up wedding comedian City six

1 and 6 because 6 is not a prime number

so much eg second among a number in a

prime number Islam so halimbawa 6 we

have two entry 2 times 3 is 6 2 & 3 are

prime numbers and then x squared Sousa

15 am an Indian attire pointing to

momentum 1 and 15 we can only use 3 & 5

if you are using prime factorization and

there

X raise to 4 so unknown comments of

vanillin dalawa we have three and then

coordinate any impede on Ababa exponents

of variable and that is squared so we

will have the GCF is 3x squared next

let's try to find the GCF of each pair

of monomials so I have here 6a and 18 a

B so for 6a by using prime factorization

we have 2 times 3 times a for 18 a B we

have 2 times 3 times 3 times a times B

so OD pink una a Hannah or Maggie is a

plant I you know malefactors na prime

numbers lump OH so 2 times 3 is 6 6

times 3 is 18 now

I know Marin's a 6 in the marin k-8 in a

B para Hasidim my 2 and 3 para her

insulin my a so you know I Baba bana 10

we will have 2 times 3 times a and then

we will multiply 2 times 3 that will

become 6a next I have here it an A and

12 a squared B so hi Napolitano my zip

tie on among a prime numbers now factors

num 10 so we have 2 & 5 2 times 5 is 10

and then a so for 12 a squared B we have

2 times 2 times 3 because 2 times 2 is 4

4 times 3 is 12 and then a squared times

B so a new comments of vanillin dalawa

we have 2 and then Perry who salon my a

but remember nifer / / a hosting on my

variable neon that is their common

variable pair of a Pagano and kohonen

and nothing you my pin Hama Baba an

exponent so we will get a not a

so Bob a banana in you and we have to

and then II now bakit hindi KO nila guys

history because wala naman three certain

a bucket in the couny legacy five Cassie

well and among pipes it will a squared B

bucket in the cannula Gracie because

Evelyn among be eaten a so we will only

get two and a and that is the GCF is 2 e

next I have here negative eight x

squared y + 16 X Y so for negative 8

since negative Y unmarried I am negative

sign and then two times two four times

so that is eight x squared times y for

16 X Y we have two x - 4 x - 8 x - 16

and then x + y so I know comments of

AnnaLynne del agua we have 2 times 2

times 2 indeed anatomy sasame you need

some tools a 16 X Y cassette along the

Monon to dunce a negative 8x squared Y

now para hasidim may come on the X

variable so again kohonen Lunetta apena

from above an exponent and that is X

same as Y so bring down a 10 in that

long to e by by not in CX and CY so we

will have now 2 x - 4 times 2 that is 8

X Y next eight a B raised to 3 or 8 eb q

+ 10 y squared b squared so for 8 a B

cube we have 2 times 2 times 2 times a

times B cube portend a squared B squared

we have 2 times 5 times a squared times

B squared so an on hormone we have - we

will not get the other tools Casa

Gallina minang students attend a squared

b squared

indeed not including a legacy 5 casa

wala naman 5 by 8 a B cube now for a

variable kakuni not a Numa Bob an

exponent and that is a verb in a man and

ma Baba IC b squared so you know kohonen

attend so we will have now 2 e and b

squared so the GCF is 2 a B squared

okay let's proceed on how are we going

to factor polynomial in omean refers to

rewriting a polynomial as a product of

polynomials of smaller degree so we will

try to factor the given polynomial using

the GCF so I have here 4x squared plus

6x so holy not in a GCF that is 2x in

factored form you GCF in Alleghany not

inches on the bus now I know not in

Cahoon a new NASA lobna parentheses

okay so puede think of a number not a

bug or think of a monomial hug me

multiply mode the resulting product will

be 4x squared so hogaya nito 2 times 2

is 4 and then the LA 1x we will add the

exponent that's why it became x squared

now back it 3 because 2 times 3 I am 6

and then since it's a lock on X yeah

that's why we have 6x another way

podrían among c4 x squared e divided

musa 2 X 4 divided 2 that is 2 x squared

divide X cap Ignasi divide Taiyo we are

subtracting the exponent if they have

the same base that's why x squared minus

1 a Toyin 2x dents a GCF not NK on again

X nalang done and then 6 divide to pay

an Ohana to c3

another example 3x squared plus 6x the

GCF is 3x Salalah gain a teensy 3x

alibis panadeine kakuni noonas Allah or

think of a monomial again so 3x and then

since x squared Y so Metallica title is

some X and then 3 times 2 that is 6 and

then we only have one X Chaya 6x Don

next 6 X raise to 4 minus 14x squared so

the GCF is 2x squared

lalla gain attention oil pan acutally

new 3x squared because 2 times 3 is 6x

squared and then x squared that will

become X raise to 4 now this is my nose

and then 2 times 7 that makes it four it

in and then since we only have x squared

that's why we have 14x squared okay

let's have the detailed solution yes you

see after they write the polynomial so

kagael and in tow Hanina very Papa

hittin a teen this is another way using

distributive property so at all a legacy

GCF see 2x and then use distributive

property gonna go there and you eat a

time some hi 2x for you to get 4x

squared at I know you get at times

Marines dance a second term or

Parramatta Hamas is 6x so iron panel not

into gagawin who annoy you GCF

Dagon attendance and Abbas pendin come

on om na ho ha mom come on wanna

monomial factor rather you know Gilligan

attends aha parentheses

next three x squared plus 6x so again

use the GC after I write the polynomial

illapis not in C 3 X and then 3 X in the

second term think of a monomial factor

which is x + - Sibylla so we will have

now 3 x times X plus 2 pi new noggin

ganyan write the GCL and then the common

monomial factor

next six X raise to 4 minus 14x squared

so same procedure buh-bah see GCF and

then enclosed by the parentheses or

or not in June 3x squared

copy the sign and then bring down seven

next I have here 7/8 times a plus 3

minus C times a plus 3 so panel not in

shape apart or so see a simple as thing

Manza who I know young GCF nil epochs in

having GCF I know you Marin Cilic are a

whole that is a plus 3 so I bababa not

in yon and then in 7a minus C e ba ba ba

Rena 10 I am

hey another example so Conan will let

you GCF young comments of vanilla that

is n plus 3 and then say 8m plus B that

is another binomial sum Johnathon

Schaech not a factor

okay another example I have here four

times three B minus 1 plus Phi B times 1

minus 3p plus 4c times 3 B minus 1 so

who mop up and say no pan unit into

muffin fact or in unison the or not

parentheses there's a middle term Nathan

I 1 minus 3p so what I see long GCF

debar so mahira so pan on Dagobah not n

we all know that 1 - 3 B is equal to

negative times the quantity of negative

1 plus 3b so panadeine gagawin yan

if a times not ensure by negative 1 come

on yaar a McGee negative 5a times

negative 1 plus 3b plus 4c times the

quantity of 3b minus 1 so i na in an

area so seam allowance at the ass the

name's not attentions by negative 1 K

and again negative 5a c1 again negative

1 C negative 3b in again positive 3 P

now in deeper in Xalapa Reijo so pan and

gagawin we will just rearrange the given

polynomial so put in a knot in song are

you saying

so panel gaga when I use in the net in

show you 3 be like ela gamer sir laughs

you minus 1 in the game sir

right so map app encino para para holly

solanum GCF so we will now have 3b minus

1 times 4 minus 5a plus 4c

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