FACTORING USING COMMON MONOMIAL FACTOR || GRADE 8 MATHEMATICS Q1
Summary
TLDRIn 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
- ๐ Understanding how to find the Greatest Common Factor (GCF) of polynomials.
- ๐ Two methods to find the GCF: Listing factors and Prime Factorization.
- ๐ข Explanation of monomials and polynomials, including their components like constants and variables.
- ๐งฉ Importance of arranging polynomials in standard form for easier factoring.
- ๐งฎ Definition of GCF: The greatest numerical factor with variables having the least degree.
- ๐ Step-by-step example of finding GCF by listing factors and using prime factorization.
- ๐ Factoring pairs of monomials using prime factorization to identify common factors.
- ๐ Applying the distributive property to factor polynomials using the GCF.
- ๐ Detailed examples of factoring various polynomials using GCF and distributive property.
- ๐ 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
๐ถ 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.
๐ข 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 12aยฒB, and negative 8xยฒy and 16xy.
โ๏ธ 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 4xยฒ + 6x and 3xยฒ + 6x. The process of using the distributive property to simplify polynomials is detailed.
๐ 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.
Mindmap
Keywords
๐กGreatest Common Factor (GCF)
๐กPrime Factorization
๐กPolynomial
๐กMonomial
๐กStandard Form
๐กCommon Monomial Factor
๐กDistributive Property
๐กVariable
๐กExponent
๐กFactoring
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
podrรญan 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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