More examples of factoring by grouping | Algebra I | Khan Academy

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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
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Пікірлер: 254

  • @Neuman357
    @Neuman35710 жыл бұрын

    Khan Academy is where I go to learn. School is where I go to repeat what Khan taught me.

  • @OneBrokenEgg

    @OneBrokenEgg

    3 жыл бұрын

    Exactly

  • @CrimsonBlood0357

    @CrimsonBlood0357

    3 жыл бұрын

    yes mr doomguy

  • @stubdto2479
    @stubdto24797 жыл бұрын

    I remember the days when i thought i was good at math

  • @DanNguyen-th5gp

    @DanNguyen-th5gp

    7 жыл бұрын

    same

  • @esmelilias

    @esmelilias

    6 жыл бұрын

    SAME

  • @jaysonheeralall8377

    @jaysonheeralall8377

    6 жыл бұрын

    Before 5th grade...

  • @shaylinclark2849

    @shaylinclark2849

    4 жыл бұрын

    FREAKING SAAAME

  • @Someone-fl3ki

    @Someone-fl3ki

    4 жыл бұрын

    SAMEEEE

  • @freeguitartips
    @freeguitartips7 жыл бұрын

    Khan academy...your contribution to humanity is simply amazing.

  • @salizman6953

    @salizman6953

    4 жыл бұрын

    Hey man how u doing now? Been three years

  • @wubsky5990

    @wubsky5990

    4 жыл бұрын

    Saliz Man hahahahahhaha

  • @wubsky5990

    @wubsky5990

    4 жыл бұрын

    Saliz Man u in grade 8?

  • @cherryzhu9646
    @cherryzhu96468 жыл бұрын

    This is very helpful, I can't understand my math teacher's accent, when I ask how to solve math problem, he always show his impatience, reluctant to help me.

  • @DanNguyen-th5gp

    @DanNguyen-th5gp

    7 жыл бұрын

    maybe he's a racist ya neva know

  • @DanNguyen-th5gp

    @DanNguyen-th5gp

    7 жыл бұрын

    go to another school m8 dont go to some school where a mexican teaches (she might have jumped the wall recently)

  • @rawr5282

    @rawr5282

    4 жыл бұрын

    That is a little racist

  • @randomsodaez293

    @randomsodaez293

    3 жыл бұрын

    @@DanNguyen-th5gp LMFAOOO

  • @ianzuzunaga4907
    @ianzuzunaga49078 жыл бұрын

    Props to you man I'd say I learned more in 10 minuets than in a week at my schools.

  • @snorlaxking1838

    @snorlaxking1838

    6 жыл бұрын

    I guess you don't learn much *minutes

  • @hamsub4798

    @hamsub4798

    6 жыл бұрын

    for me a year

  • @rawr5282

    @rawr5282

    4 жыл бұрын

    Same

  • @jacobtica2840

    @jacobtica2840

    3 жыл бұрын

    Facts!!!!!

  • @J0rdan069

    @J0rdan069

    5 ай бұрын

    ​@@snorlaxking1838That looks like an obvious typo.

  • @krislona1
    @krislona19 жыл бұрын

    i feel like he's making it even harder than it needs to be

  • @jocelynlin6044

    @jocelynlin6044

    8 жыл бұрын

    EXACTLY.

  • @pleasesetmeonfire1166

    @pleasesetmeonfire1166

    7 жыл бұрын

    krislon lona Actually, this is the EASY way. If you do it the HARD way, like my past experience, they make you factor the first number in front of x^2, AND the last number. Then you mix and match the factors, use the (fx + g)(hx + j) method to test it. If you end up with the equation you start with, you're right. If not, mix up the numbers and try again. It's a guess and check system that takes FOREVER

  • @hectortapia8413

    @hectortapia8413

    6 жыл бұрын

    the cake method is faster than this

  • @Miranda_Writes

    @Miranda_Writes

    5 жыл бұрын

    Agreed

  • @gumaropedro373

    @gumaropedro373

    5 жыл бұрын

    Khan academy always do that. This way of explanation is too complex. They do not realize that if people comes here is because they do not understand the way their teachers teach them so they need a more basic explanation.

  • @TheDarkMaster02
    @TheDarkMaster026 жыл бұрын

    Why did they have to introduce the alphabet into math?

  • @HotKritiskais

    @HotKritiskais

    3 жыл бұрын

    KNOWLEDGE obviously

  • @adityashivapooja2681

    @adityashivapooja2681

    3 жыл бұрын

    For abstraction and higher-level thinking. A variable or "letter" represents a number in math. It can represent ANY real number, such as 1 or -3 or 0.5 or pi or 2/3 etc. When we work with variables, we are looking at an abstract equation or expression that can be used to work with numbers or play with numbers and number theory. Hope this is clear :)

  • @emilym2409
    @emilym24093 жыл бұрын

    Thanks for this video! One note - towards the end of the video, the (fh)x needs to be (fh)x^2. Thanks!

  • @lucasloy7587

    @lucasloy7587

    2 жыл бұрын

    Thank you, I literally came here to say the same thing!

  • @geoffreycarre6256

    @geoffreycarre6256

    2 жыл бұрын

    thank you i was sure it was a mistake, but they correct it usually with a comment on the video, so i had some doubt !

  • @s0ap388
    @s0ap3886 жыл бұрын

    5:27 - i must admit it is a really good fart

  • @saaad

    @saaad

    5 жыл бұрын

    That is a good fart

  • @hannazakiy9861

    @hannazakiy9861

    4 жыл бұрын

    lol

  • @lithium1770

    @lithium1770

    3 жыл бұрын

    Lol

  • @pleasesetmeonfire1166
    @pleasesetmeonfire11667 жыл бұрын

    Another easy way with checking your work (rather than fx + g and hx + j) is something called F.O.I.L. F stands for First. Multiply the two first numbers. For example, in (x + 1)(6x + 1) you would multiply x • 6x and get 6x^2 (6x squared). O stands for Outside. Multiply the outside numbers. For example, in (x + 1)(6x + 1) you would multiply the outside terms, x • 1, and get 1x. I stands for Inside. Multiply the inside numbers. For example, in (x + 1)(6x + 1) you would multiply the inside terms, 1 • 6x, and get 6x. L stands for last. Multiply the last numbers. For example, in (x + 1)(6x +1) you would multiply the last terms, 1 • 1, and get 1. Now you have 6x^2 + 1x + 6x + 1. Combine like terms (1x and 6x) and get 7x. Now the equation is 6x^2 + 7x + 1. If the equation you got from F.O.I.L is the one you began with, you factored everything correctly. If not, you did it wrong. Hope I made that simple enough

  • @moisekazembe7894
    @moisekazembe78943 жыл бұрын

    With school you study and throw your notes and books , with Khan you study and come anytime to still find your lessons . Khan academy is our lifetime brain.

  • @dawnmarie7818
    @dawnmarie78189 жыл бұрын

    Hi! I just want to say THANK YOU SO MUCH for these videos! They are incredibly helpful and useful! And very explanatory, so I really appreciate it :) thank you for making these!

  • @darrenpeterson5741
    @darrenpeterson574110 жыл бұрын

    I think the problem at 12:20 is awesome for some reason. Goes from looking at a confusing problem to simplicity in half a second. lol

  • @allentowncola937
    @allentowncola9377 жыл бұрын

    I feel so great when I understand mathematics.Thank you so much Sal.

  • @lucasloy7587
    @lucasloy75872 жыл бұрын

    For anyone wondering at 9:35 in he should have put (fh)x² instead of (fh)x.

  • @connor7599

    @connor7599

    2 жыл бұрын

    Thankyou, I thought I was going crazy ;-;

  • @isaacmalsch635
    @isaacmalsch6358 жыл бұрын

    I want lays cheese and sour cream chips rn

  • @snorlaxking1838

    @snorlaxking1838

    6 жыл бұрын

    My man

  • @Red-cq7ld

    @Red-cq7ld

    6 жыл бұрын

    me too

  • @kobimizrahi9397
    @kobimizrahi93976 жыл бұрын

    3:46 the order actually doesn’t matter! I could do 4x^2-3x+28x-21=x(4x-3)+7(x-3)=(x+7)(4x-3)

  • @CrimsonBlood0357

    @CrimsonBlood0357

    3 жыл бұрын

    ???????

  • @mandakhbayar.m8298

    @mandakhbayar.m8298

    2 жыл бұрын

    the (4x-3) and the (x-3) are not the same, so you can"t just (x+7)(4x-3) it..... i mean am i missing something?

  • @nolanvondracek3463
    @nolanvondracek346311 жыл бұрын

    I am so grateful you do this for us Khan, even though you must have better things to do with that amazing brain of yours. Thanks for posting ALL these helpful videos to teach the world math. I'm a 6th grader trying to learn Algebra over the summer and I don't think I would have passed without you.

  • @RydinTheBlaze
    @RydinTheBlaze10 жыл бұрын

    I love you so much I was always good at factoring like i was a pro but you just made it like ten times faster and easier thank you so much!

  • @shanthavinageswaran2772
    @shanthavinageswaran27722 жыл бұрын

    THANK YOU SO MUCH I TOTALLY FORGOT HOW TO DO IT AND MY HW IS DUE IN A COUPLE OF HOURS!!!! THANK YOUUU

  • @Manima108
    @Manima1085 жыл бұрын

    I stg this man is my hero he made me learn more than I did in a week of ib classes

  • @justaguy8396
    @justaguy83967 жыл бұрын

    As always your lessons are wonderful and insightful

  • @danielredziniak2996
    @danielredziniak29969 жыл бұрын

    thank you so much i have a quiz on this tomarrow and thank u again.

  • @admiremakombe4278
    @admiremakombe42787 жыл бұрын

    help factorise completely 6a - 6bd -3bc +8ad

  • @mspeneney
    @mspeneney5 жыл бұрын

    Thank you very much ! It helps a lot !.

  • @rupok93
    @rupok9313 жыл бұрын

    I love your videos, they are very useful and extremely professional. Very proud of someone with origins from Bangladesh (like me) has spread education like this worldwide. Thank you again for your easy explanations and wide range of material that help me out so much in high school.

  • @FareedChughtai
    @FareedChughtai12 жыл бұрын

    Made it so simple.. Respects!

  • @Nircode
    @Nircode3 жыл бұрын

    Khan Academy, brilliant!! Thanks man

  • @TheDanksNewGroove
    @TheDanksNewGroove11 жыл бұрын

    This dudes strategy makes soooo much more sense then the way my Algebra teacher taught me! :D

  • @danmadefurniture
    @danmadefurniture5 жыл бұрын

    loved the bit at the end where you explained how it works

  • @gawni1612
    @gawni16123 жыл бұрын

    You are saving my life dude. Love you.

  • @MichaelAllen14
    @MichaelAllen147 жыл бұрын

    Thanks for uploading this video. It was very helpful.

  • @pranavlonaree6732
    @pranavlonaree67326 жыл бұрын

    This is perfect to me!

  • @vishula1
    @vishula110 жыл бұрын

    (Fx) x (hx) = Fhx^2 Isn't it?

  • @joejohnson3707

    @joejohnson3707

    9 жыл бұрын

    I think so

  • @Manima108

    @Manima108

    5 жыл бұрын

    that's what I was thinking

  • @direagan8778

    @direagan8778

    5 жыл бұрын

    @@merge3550 f and h have nothing to do with function notation. They represent some integer. Sunny trees is right.

  • @andreeaa1228
    @andreeaa122811 жыл бұрын

    Thanks! This was soooo helpful!

  • @pringlescan9174
    @pringlescan91746 жыл бұрын

    This is extremely helpful cuz even when we know how to factor in other ways, we're still supposed to use this for a test.

  • @NauTzZz
    @NauTzZz11 жыл бұрын

    don't know how my teacher factors like lightning

  • @shrabastiadhya
    @shrabastiadhya3 жыл бұрын

    WOW. Very nice explanation. ALL DOUBTS CLEARED. 😌

  • @Debedeb
    @Debedeb12 жыл бұрын

    I want to let you know how I appreciate you doing these videos, you are God Sent ;)

  • @esmelilias
    @esmelilias6 жыл бұрын

    NICE! COOL EXPLANATION!

  • @Coffee19feen
    @Coffee19feen12 жыл бұрын

    Thanks! It's clear to me now :)

  • @InshasChoice
    @InshasChoice8 жыл бұрын

    This method comes into hand, but for the worth of factorising, this is way too complicating.

  • @battab80
    @battab8011 жыл бұрын

    You've saved me! Thank you so much :D

  • @RaselRanamath
    @RaselRanamath3 жыл бұрын

    Just awesome 👌

  • @choi_otteryj4287
    @choi_otteryj42877 жыл бұрын

    Understand this more, more than my math teacher at school

  • @kenshinala1984
    @kenshinala19847 жыл бұрын

    Thnx for making these

  • @ultimate-brick-films
    @ultimate-brick-films3 жыл бұрын

    This is better than my math book even after 7 years it was posted

  • @lewirthlindatuin209
    @lewirthlindatuin2093 жыл бұрын

    Sensei Thank you VERY MUCH!!!!!!!!!!!!!!!!!!!!!!!!

  • @kenal9719
    @kenal97199 жыл бұрын

    This is a good math.

  • @MariaOrtiz-wl1op
    @MariaOrtiz-wl1op8 жыл бұрын

    I do appreciate the concern at 6:14

  • @subirsanyal7044
    @subirsanyal70444 жыл бұрын

    I really liked it

  • @mabus2007
    @mabus200713 жыл бұрын

    have you heard of the curtain method for these type of problems? can you do a video on that as well?

  • @scottcollinswhataboutmonst6278
    @scottcollinswhataboutmonst62782 жыл бұрын

    Even though Khan Acadeny is an excellent video, the commucation would be a bit much for beiginners. When i was in school, I always leaarned to multiply the first and last number. You then find the factors of those numbers. You look at the last number to the problem. By the last number, you can determine if y0u should add or subtract the factors! This method usually helped me in ;the past,

  • @zacharymorritt
    @zacharymorritt6 жыл бұрын

    When the video teaches you better than the class you're taking in school.

  • @somewhereonthebottom
    @somewhereonthebottom11 жыл бұрын

    Ohmygod thank you so much I finally understand!

  • @akiratokyodesu6266
    @akiratokyodesu62665 жыл бұрын

    I LOVE THIS GUY

  • @gbmsg282
    @gbmsg2823 жыл бұрын

    Thank you thank you thank you!

  • @thebestmathacademy8838
    @thebestmathacademy8838 Жыл бұрын

    Excellent video

  • @frosty65596559
    @frosty6559655911 жыл бұрын

    thts basically my life 2 :)....thx so much

  • @jdjed24
    @jdjed247 жыл бұрын

    Hey Sal, do you have any lessons regarding how to factor this sort of equation x^2 - y^2 - 3x + 3y Am having trouble understanding how to do this

  • @DerpsterIV

    @DerpsterIV

    7 жыл бұрын

    you cant

  • @jdjed24

    @jdjed24

    7 жыл бұрын

    jakiN apparently you can

  • @teikiribati2
    @teikiribati210 жыл бұрын

    to make it short and also not to get confuse of other x's aswell

  • @Ja12Grizz02
    @Ja12Grizz028 жыл бұрын

    Thank you I passed my exam

  • @chesskhan
    @chesskhan13 жыл бұрын

    I completely forgot about this trick when I was doing my summer homework, thanks soooooooooooooooooooooooooooooo much Salman! (It's almost like Kung Fu, eh?)

  • @andyandanadraws
    @andyandanadraws5 жыл бұрын

    Thank U VERY VERY VERY VERY VERY VERY VERY MUCH

  • @GDInspirations
    @GDInspirations8 жыл бұрын

    Easy way to think about factors = simplify 4 and - 21 -> 2*2*(-7)*(3) , now combine them in different ways and choose the one that works for example here 28-3 is perfect = 7*4 = 28 and multiply that by 3 ypu get 84 !

  • @kenal9719
    @kenal97199 жыл бұрын

    This math is good.

  • @adaleiasantos5911
    @adaleiasantos59114 жыл бұрын

    God bless you king.

  • @castledestoyerz6190
    @castledestoyerz61902 жыл бұрын

    Thank you

  • @jordiwapachee9487
    @jordiwapachee948710 жыл бұрын

    Show us the basics from start to finish from all mixed number from high to low

  • @itsladak
    @itsladak13 жыл бұрын

    YOU SAVED ME FROM FAILING UR AWSOME MAN

  • @ATLGETREADY4ME
    @ATLGETREADY4ME10 жыл бұрын

    Can you please tell where i can find a time table sheet and a copy of the red Baron's book, which i can't remeber the title of right now. I need it for a college assessment test

  • @PnutDemanciaTKO
    @PnutDemanciaTKO11 жыл бұрын

    Aced so many math test because of this guy. GG.

  • @bigblockelectra
    @bigblockelectra5 жыл бұрын

    5:03 How you do you know when to factor out a negative or positive number? I thought factoring was always 'self-correcting' in that you could do either and the answer would always be the same. If you factor out a positive 3 at this point, the answer is wrong (-x-7). What is the rule? What is the rule for one positive and one negative number?

  • @lavatrout
    @lavatrout14 жыл бұрын

    can you make a video showing how to factor trinomials with two variables like: (a^2) + (6ab) + (8b^2)

  • @Golden_Tortoise
    @Golden_Tortoise3 жыл бұрын

    I believe its a * c and a + c not a * b at 1:50 but he did the math correct anyways

  • @marinacam2755

    @marinacam2755

    3 жыл бұрын

    yea, we learned it as the AC method, so I was a bit confused

  • @ceilingphans7332
    @ceilingphans73325 жыл бұрын

    thank you :)

  • @omarosman1966
    @omarosman19668 жыл бұрын

    i still dont fucken get it

  • @mycesansalatielu6238

    @mycesansalatielu6238

    8 жыл бұрын

    +Omar Osman your'e not the only one

  • @maisiecatalina1116

    @maisiecatalina1116

    8 жыл бұрын

    Shut up both of u

  • @sujayr9327

    @sujayr9327

    7 жыл бұрын

    maisie catalina mom

  • @amberdominguezz
    @amberdominguezz2 жыл бұрын

    i remember when i had a crush on this guy cuz of a voice…i still do

  • @mrhnm
    @mrhnm14 жыл бұрын

    @gf1605 It is important to understand how things are arrivied at. All the Quadratic Formula is, is completeing the square

  • @sarahcecogo3212
    @sarahcecogo32123 жыл бұрын

    thankyou

  • @dyBAR25
    @dyBAR2512 жыл бұрын

    Great video! It helped me but i couldnt get the answers from the book. Therefore, if for example you would get an answer of (x+7)(4x-8). The completely factored answer would not be (x+7)(4x-8) , which i thought....But it would be 4(x+7) (x-2). Just a thought....

  • @16afroehlich
    @16afroehlich12 жыл бұрын

    i had the same situation!!!

  • @eachneverydaynosleep
    @eachneverydaynosleep13 жыл бұрын

    NIce shit brah loved it teach better than my teacher brah

  • @bboyginseng
    @bboyginseng2 жыл бұрын

    I may be missing something but at 9:35, when you distribute (fx) with (hx), shouldn't it be (fhx^2)? Not just (fhx)? I am confused as to why it's just (fhx).

  • @connor7599

    @connor7599

    2 жыл бұрын

    WHY HAS NOBODY ANSWERED THIS? I'm confused too 😭

  • @DarklightALBANIA
    @DarklightALBANIA12 жыл бұрын

    @lavatrout It looks hard but is really easy just : divide 6ab into 4ab +2ab Than hopefully you should know how to factor by grouping

  • @FernandoFlores-ut8ic
    @FernandoFlores-ut8ic7 жыл бұрын

    LOVE YA POLYS!!!!!

  • @Sabuj559
    @Sabuj55912 жыл бұрын

    Can anyone tell me the answer of this question? What is the GCF of the terms of the polynomial x^a+x^b+x^c given that a,b, and c are all positive integers, and a>b>c? My teacher told me about the solution, but as usual, it went way above my head. Can anyone please explain me the solution?

  • @38dhruvthakkar76
    @38dhruvthakkar762 жыл бұрын

    the sum is not hard it was explained in a complex way

  • @j_wolf_cuber153
    @j_wolf_cuber1533 жыл бұрын

    does this work on all quadratics or just specific ones?

  • @BlindmanShady
    @BlindmanShady12 жыл бұрын

    In almost all cases, order DOES NOT matter. I tutor math, I've shown it to my students.

  • @jl7986
    @jl79869 жыл бұрын

    Khan Academy I'm here because your website isn't displaying the videos in the content frame. The loading icon just revolves ad infinitum. It's been like this pretty much all day, it worked for about an hour then stopped working again. Any idea what the problem is or when it'll be fixed? :-\

  • @DanNguyen-th5gp

    @DanNguyen-th5gp

    7 жыл бұрын

    wats sad is that im the only one that replied too this guy^^^^

  • @catatocat7786

    @catatocat7786

    6 жыл бұрын

    Danny Nguyen whats the sad part

  • @WassupDL66
    @WassupDL6611 жыл бұрын

    Sal you should use the box method and teach that to your viewers.

  • @SunggukLim
    @SunggukLim8 жыл бұрын

    When I was a middle school student, I had gave up 'Math' subject. because of this.

  • @nobojitchutia861
    @nobojitchutia8615 жыл бұрын

    Nice😔

  • @AT-bq6gs
    @AT-bq6gs6 жыл бұрын

    At 9.57 doesn't it become x2?

  • @Moon-fv7kf
    @Moon-fv7kf Жыл бұрын

    What if it is: 4x^2+25x+21? What numbers multiplied would be 84 and added could make 25?

  • @selenamccleery8979
    @selenamccleery897911 жыл бұрын

    So how would you find the zeros of 3x^5-15x^4+26x^3-9x^2-13x+5......

  • @chrisarrow
    @chrisarrow3 жыл бұрын

    9:35 shouldn't that be (fh)x^2 ?

  • @Eat_Pi

    @Eat_Pi

    3 жыл бұрын

    Nice catch! It definitely should be, he forgot to square it

  • @ThePunchingpuddle
    @ThePunchingpuddle7 жыл бұрын

    Can you guys make a way more advanced factoring lesson because I really need help with the stuff I'm doing it's like way more advanced algebra 2 problems

  • @veryberrytravels
    @veryberrytravels4 жыл бұрын

    how would you solve 2x^2+5x+6 using this method? I tried doing 2x6=12 but nothing multiplies evenly to multiply to 12 and add up to 5

  • @pieinthesky1105

    @pieinthesky1105

    3 жыл бұрын

    Make sure to multiply by the greatest common factor as your first step. Sometimes when a problem is this complex you must divide by your larger number and then add everything together.

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