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.
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
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.
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 :)
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
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,
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!
what about polynomials with four terms and no common factor where you have to factor by grouping such as 3x^3 - x^2 +18x - 6? To explain, you would group the terms and then factor what you can from each term and factor out the common factor
You can do a generalized "proof" of the factoriation too: ax^2 + bx + c j*k = a*c ax^2 + jx + kx+c j+k = b ax(x+j/a) + k(x+c/k) k/a = c/j= j/a = c/k = f ax(x+f) + k(x+f) you get f by mixing around (ax+k)(x+f) with j*k = a*c ax^2 + bx + c = (ax+k)(x+f) This explains how grouping works with any polynomial on the form ax^2 + bx + c and it makes it easy to explain how it works too. Its all about finding how to split the b into a common multipoom of a*c.
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 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.
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 !
Why are you saying a + b and (a)(b) and then adding/multiplying a with c? On the first example, the -21 is C, not B. It's ax^2 + bx + c... Not ax^2 + cx + b.
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?
Kindly make everything clear, if you are going to make quadratic then it means you must have the square value and as you are multiplying the two value of 'x' you simply ignored this thing that ' x*x ' will be ' x² ' , kindly ponder upon that if you are educating online, it will help others or destroy other's basics.
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).
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?
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.
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 completely forgot about this trick when I was doing my summer homework, thanks soooooooooooooooooooooooooooooo much Salman! (It's almost like Kung Fu, eh?)
Khan Academy is where I go to learn. School is where I go to repeat what Khan taught me.
Exactly
yes mr doomguy
I remember the days when i thought i was good at math
same
SAME
Before 5th grade...
FREAKING SAAAME
SAMEEEE
Khan academy...your contribution to humanity is simply amazing.
Hey man how u doing now? Been three years
Saliz Man hahahahahhaha
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.
maybe he's a racist ya neva know
go to another school m8 dont go to some school where a mexican teaches (she might have jumped the wall recently)
That is a little racist
@@DanNguyen-th5gp LMFAOOO
Props to you man I'd say I learned more in 10 minuets than in a week at my schools.
I guess you don't learn much
*minutes
for me a year
Same
Facts!!!!!
@@snorlaxking1838That looks like an obvious typo.
i feel like he's making it even harder than it needs to be
EXACTLY.
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
the cake method is faster than this
Agreed
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?
KNOWLEDGE obviously
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 :)
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
Thanks for this video! One note - towards the end of the video, the (fh)x needs to be (fh)x^2. Thanks!
Thank you, I literally came here to say the same thing!
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 !
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,
5:27 - i must admit it is a really good fart
That is a good fart
lol
Lol
For anyone wondering at 9:35 in he should have put (fh)x² instead of (fh)x.
Thankyou, I thought I was going crazy ;-;
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!
Somehow... this still helps me today. Kahn Academy is magic
I feel so great when I understand mathematics.Thank you so much Sal.
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
what about polynomials with four terms and no common factor where you have to factor by grouping such as 3x^3 - x^2 +18x - 6? To explain, you would group the terms and then factor what you can from each term and factor out the common factor
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)
???????
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?
You can do a generalized "proof" of the factoriation too:
ax^2 + bx + c j*k = a*c
ax^2 + jx + kx+c j+k = b
ax(x+j/a) + k(x+c/k) k/a = c/j= j/a = c/k = f
ax(x+f) + k(x+f) you get f by mixing around
(ax+k)(x+f) with j*k = a*c
ax^2 + bx + c = (ax+k)(x+f)
This explains how grouping works with any polynomial on the form ax^2 + bx + c
and it makes it easy to explain how it works too. Its all about finding how to split the b into a common multipoom of a*c.
I stg this man is my hero he made me learn more than I did in a week of ib classes
(Fx) x (hx) = Fhx^2
Isn't it?
I think so
that's what I was thinking
@@merge3550 f and h have nothing to do with function notation. They represent some integer. Sunny trees is right.
thank you so much i have a quiz on this tomarrow and thank u again.
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 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.
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!
I want lays cheese and sour cream chips rn
My man
me too
THANK YOU SO MUCH I TOTALLY FORGOT HOW TO DO IT AND MY HW IS DUE IN A COUPLE OF HOURS!!!! THANK YOUUU
This dudes strategy makes soooo much more sense then the way my Algebra teacher taught me! :D
help factorise completely 6a - 6bd -3bc +8ad
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.
i still dont fucken get it
+Omar Osman your'e not the only one
Shut up both of u
maisie catalina mom
As always your lessons are wonderful and insightful
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 !
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
you cant
jakiN apparently you can
Why are you saying a + b and (a)(b) and then adding/multiplying a with c? On the first example, the -21 is C, not B. It's ax^2 + bx + c... Not ax^2 + cx + b.
Khan Academy, brilliant!! Thanks man
You are saving my life dude. Love you.
I want to let you know how I appreciate you doing these videos, you are God Sent ;)
This method comes into hand, but for the worth of factorising, this is way too complicating.
Thank you very much ! It helps a lot !.
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?
Kindly make everything clear, if you are going to make quadratic then it means you must have the square value and as you are multiplying the two value of 'x' you simply ignored this thing that ' x*x ' will be ' x² ' , kindly ponder upon that if you are educating online, it will help others or destroy other's basics.
WOW. Very nice explanation. ALL DOUBTS CLEARED. 😌
Understand this more, more than my math teacher at school
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).
WHY HAS NOBODY ANSWERED THIS?
I'm confused too 😭
I really liked it
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?
This is perfect to me!
thank you sal, atm im taking gr 12 advanced functions without taking gr11 functions, so im teaching my self gr11 while taking gr 12 >.
Show us the basics from start to finish from all mixed number from high to low
have you heard of the curtain method for these type of problems? can you do a video on that as well?
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
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.
loved the bit at the end where you explained how it works
Interesting 0:15
Made it so simple.. Respects!
to make it short and also not to get confuse of other x's aswell
This is better than my math book even after 7 years it was posted
Thanks for uploading this video. It was very helpful.
Sensei Thank you VERY MUCH!!!!!!!!!!!!!!!!!!!!!!!!
don't know how my teacher factors like lightning
Thank you I passed my exam
does this work on all quadratics or just specific ones?
I do appreciate the concern at 6:14
NICE! COOL EXPLANATION!
9:35 shouldn't that be (fh)x^2 ?
Nice catch! It definitely should be, he forgot to square it
I believe its a * c and a + c not a * b at 1:50 but he did the math correct anyways
yea, we learned it as the AC method, so I was a bit confused
Aced so many math test because of this guy. GG.
This is a good math.
Just awesome 👌
can you make a video showing how to factor trinomials with two variables like:
(a^2) + (6ab) + (8b^2)
Excellent video
Thnx for making these
Thank you
In almost all cases, order DOES NOT matter. I tutor math, I've shown it to my students.
@lavatrout It looks hard but is really easy just : divide 6ab into 4ab +2ab
Than hopefully you should know how to factor by grouping
i remember when i had a crush on this guy cuz of a voice…i still do
This math is good.
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....
Thank U VERY VERY VERY VERY VERY VERY VERY MUCH
Thank you thank you thank you!
Thanks! It's clear to me now :)
Sal you should use the box method and teach that to your viewers.
@gf1605 It is important to understand how things are arrivied at. All the Quadratic Formula is, is completeing the square
YOU SAVED ME FROM FAILING UR AWSOME MAN
What if it is: 4x^2+25x+21?
What numbers multiplied would be 84 and added could make 25?
God bless you king.
I LOVE THIS GUY
So how would you find the zeros of 3x^5-15x^4+26x^3-9x^2-13x+5......
Thanks! This was soooo helpful!
When the video teaches you better than the class you're taking in school.
You've saved me! Thank you so much :D
thankyou
25 what happened to be in the equation of a + b + C equals 0
Maria Ortiz I don't think you should do math.
why is it a times b shouldn't be a times c
Was thinking the same thing, but nobody replied to you :/ lol
same..
ikr
I’m thinking the same thing
It is not because when you have a number of that value mixed with a letter, the answer must always be multiplied by the greatest common factor.
I completely forgot about this trick when I was doing my summer homework, thanks soooooooooooooooooooooooooooooo much Salman! (It's almost like Kung Fu, eh?)
2:26
*-2 + 2 = -40*
He said -2+42=40 :/
Shamin Abraham after that he says 2+ (-2)=-40
thank you :)
At 9.57 doesn't it become x2?
thts basically my life 2 :)....thx so much