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
Khan Academy is where I go to learn. School is where I go to repeat what Khan taught me.
@OneBrokenEgg
3 жыл бұрын
Exactly
@CrimsonBlood0357
3 жыл бұрын
yes mr doomguy
I remember the days when i thought i was good at math
@DanNguyen-th5gp
7 жыл бұрын
same
@esmelilias
6 жыл бұрын
SAME
@jaysonheeralall8377
6 жыл бұрын
Before 5th grade...
@shaylinclark2849
4 жыл бұрын
FREAKING SAAAME
@Someone-fl3ki
4 жыл бұрын
SAMEEEE
Khan academy...your contribution to humanity is simply amazing.
@salizman6953
4 жыл бұрын
Hey man how u doing now? Been three years
@wubsky5990
4 жыл бұрын
Saliz Man hahahahahhaha
@wubsky5990
4 жыл бұрын
Saliz Man u in grade 8?
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
7 жыл бұрын
maybe he's a racist ya neva know
@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
4 жыл бұрын
That is a little racist
@randomsodaez293
3 жыл бұрын
@@DanNguyen-th5gp LMFAOOO
Props to you man I'd say I learned more in 10 minuets than in a week at my schools.
@snorlaxking1838
6 жыл бұрын
I guess you don't learn much *minutes
@hamsub4798
6 жыл бұрын
for me a year
@rawr5282
4 жыл бұрын
Same
@jacobtica2840
3 жыл бұрын
Facts!!!!!
@J0rdan069
5 ай бұрын
@@snorlaxking1838That looks like an obvious typo.
i feel like he's making it even harder than it needs to be
@jocelynlin6044
8 жыл бұрын
EXACTLY.
@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
6 жыл бұрын
the cake method is faster than this
@Miranda_Writes
5 жыл бұрын
Agreed
@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.
Why did they have to introduce the alphabet into math?
@HotKritiskais
3 жыл бұрын
KNOWLEDGE obviously
@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 :)
Thanks for this video! One note - towards the end of the video, the (fh)x needs to be (fh)x^2. Thanks!
@lucasloy7587
2 жыл бұрын
Thank you, I literally came here to say the same thing!
@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 !
5:27 - i must admit it is a really good fart
@saaad
5 жыл бұрын
That is a good fart
@hannazakiy9861
4 жыл бұрын
lol
@lithium1770
3 жыл бұрын
Lol
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
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.
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!
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
I feel so great when I understand mathematics.Thank you so much Sal.
For anyone wondering at 9:35 in he should have put (fh)x² instead of (fh)x.
@connor7599
2 жыл бұрын
Thankyou, I thought I was going crazy ;-;
I want lays cheese and sour cream chips rn
@snorlaxking1838
6 жыл бұрын
My man
@Red-cq7ld
6 жыл бұрын
me too
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
3 жыл бұрын
???????
@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?
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.
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!
THANK YOU SO MUCH I TOTALLY FORGOT HOW TO DO IT AND MY HW IS DUE IN A COUPLE OF HOURS!!!! THANK YOUUU
I stg this man is my hero he made me learn more than I did in a week of ib classes
As always your lessons are wonderful and insightful
thank you so much i have a quiz on this tomarrow and thank u again.
help factorise completely 6a - 6bd -3bc +8ad
Thank you very much ! It helps a lot !.
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.
Made it so simple.. Respects!
Khan Academy, brilliant!! Thanks man
This dudes strategy makes soooo much more sense then the way my Algebra teacher taught me! :D
loved the bit at the end where you explained how it works
You are saving my life dude. Love you.
Thanks for uploading this video. It was very helpful.
This is perfect to me!
(Fx) x (hx) = Fhx^2 Isn't it?
@joejohnson3707
9 жыл бұрын
I think so
@Manima108
5 жыл бұрын
that's what I was thinking
@direagan8778
5 жыл бұрын
@@merge3550 f and h have nothing to do with function notation. They represent some integer. Sunny trees is right.
Thanks! This was soooo helpful!
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.
don't know how my teacher factors like lightning
WOW. Very nice explanation. ALL DOUBTS CLEARED. 😌
I want to let you know how I appreciate you doing these videos, you are God Sent ;)
NICE! COOL EXPLANATION!
Thanks! It's clear to me now :)
This method comes into hand, but for the worth of factorising, this is way too complicating.
You've saved me! Thank you so much :D
Just awesome 👌
Understand this more, more than my math teacher at school
Thnx for making these
This is better than my math book even after 7 years it was posted
Sensei Thank you VERY MUCH!!!!!!!!!!!!!!!!!!!!!!!!
This is a good math.
I do appreciate the concern at 6:14
I really liked it
have you heard of the curtain method for these type of problems? can you do a video on that as well?
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,
When the video teaches you better than the class you're taking in school.
Ohmygod thank you so much I finally understand!
I LOVE THIS GUY
Thank you thank you thank you!
Excellent video
thts basically my life 2 :)....thx so much
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
7 жыл бұрын
you cant
@jdjed24
7 жыл бұрын
jakiN apparently you can
to make it short and also not to get confuse of other x's aswell
Thank you I passed my exam
I completely forgot about this trick when I was doing my summer homework, thanks soooooooooooooooooooooooooooooo much Salman! (It's almost like Kung Fu, eh?)
Thank U VERY VERY VERY VERY VERY VERY VERY MUCH
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 !
This math is good.
God bless you king.
Thank you
Show us the basics from start to finish from all mixed number from high to low
YOU SAVED ME FROM FAILING UR AWSOME MAN
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
Aced so many math test because of this guy. GG.
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?
can you make a video showing how to factor trinomials with two variables like: (a^2) + (6ab) + (8b^2)
I believe its a * c and a + c not a * b at 1:50 but he did the math correct anyways
@marinacam2755
3 жыл бұрын
yea, we learned it as the AC method, so I was a bit confused
thank you :)
i still dont fucken get it
@mycesansalatielu6238
8 жыл бұрын
+Omar Osman your'e not the only one
@maisiecatalina1116
8 жыл бұрын
Shut up both of u
@sujayr9327
7 жыл бұрын
maisie catalina mom
i remember when i had a crush on this guy cuz of a voice…i still do
@gf1605 It is important to understand how things are arrivied at. All the Quadratic Formula is, is completeing the square
thankyou
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....
i had the same situation!!!
NIce shit brah loved it teach better than my teacher brah
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
2 жыл бұрын
WHY HAS NOBODY ANSWERED THIS? I'm confused too 😭
@lavatrout It looks hard but is really easy just : divide 6ab into 4ab +2ab Than hopefully you should know how to factor by grouping
LOVE YA POLYS!!!!!
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?
the sum is not hard it was explained in a complex way
does this work on all quadratics or just specific ones?
In almost all cases, order DOES NOT matter. I tutor math, I've shown it to my students.
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
7 жыл бұрын
wats sad is that im the only one that replied too this guy^^^^
@catatocat7786
6 жыл бұрын
Danny Nguyen whats the sad part
Sal you should use the box method and teach that to your viewers.
When I was a middle school student, I had gave up 'Math' subject. because of this.
Nice😔
At 9.57 doesn't it become x2?
What if it is: 4x^2+25x+21? What numbers multiplied would be 84 and added could make 25?
So how would you find the zeros of 3x^5-15x^4+26x^3-9x^2-13x+5......
9:35 shouldn't that be (fh)x^2 ?
@Eat_Pi
3 жыл бұрын
Nice catch! It definitely should be, he forgot to square it
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
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
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.