[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 thank you for watching this video I hope you learned something don't forget to Like subscribe and hit the bell button so our wall my channel just keep on watching