Thank you Mr. Anderson. I can't tell you how frustrated I was getting when I was doing my homework using my professor's horrible explanation (which wasn't one at all). You saved my night.
3:00 What kind of long division is that?I am from India and I have definitely not done something like this and if I do my maths teacher will give me zero. Edit: I was a lot younger when I wrote this comment. But now after getting into high level Calculus and stuff, I have understood the easiness of this method. But due to the procedure being beaten in my head, I still find doing full long division quicker because I am at the point I can do it mindlessly.
Maybe drink a little water before you record such a long video next time! Hey, don't strain yourself, alright? Please take care of yourself ^_^ Thank you for the video! I understood it very well
My teacher is a good one, but he goes so quickly. This really helped me understand the factor theorem, and what it actually means. I saw the process of doing x-1)(2x^2-x... thank you for making this, you're a good teacher
Explained it WAY better than my math teacher did, she gives terrible notes. She moves fast and doesn't explain much. Thank you so very much, you should continue making awesome videos like this one!
Randy, please explain to me how to aproach a polynomial when the first 3 terms have powers of 4,3 and 2 respectively, instead of beginning with the cubed term.
If we are dividing by x-1, then the "k" is 1. Thus, the remainder is the same as the value f(1). In the case of this example, f(1)=0, which was the remainder you got after you divided. Make sense?
What happens if one of the coefficients of the polynomial is unknown but they give us the factor of that polynomial? How do we find the unknown coefficient?
Where did your inspiration come from to share your math knowledge with the internet audience? Nice tutorial btw although I don't understand fully the part where you factored . I'll have watch a how to factor video to refresh my memory.
hey thankyou for the vid. im not good at maths could you please explain how you get the quadratic after proving x-1 is a factor. please please i cant fail my maths exam. x
The quadratic (2x^2 - x - 6) was factored into (2x + 3)(x - 2) in the second line, if you're still wondering. He just used the normal thinking method for that, nothing special.
@arvin Actually it's a bit long procedure which we do in rough portion, So in 2x^2-x-6 , we will multiply the last value which is (6) to the coefficient of first term which is (2) with x^2.. right? We get '12' , Now we find factors of this 12, So by doing it we get 2×2×3 as factors of 12! Now you need to have two numbers such that it forms the middle value which '-x' , surely you have to take the highest one number to be negative and the other to be positive, so that our subtraction work is done ✅ and when we get the result it should include (-) sign with it. So 2×2×3 can be written as 4×3.. ok? These two values are for the middle term which is (-x), so by writing -4x+3x we will get the same (-x) value!! ..so this is correct.. now we will add this in place of our middle term value, so our expression will be like that: = (x-1) ( 2x^2 - 4x + 3x - 6) Now, we will take common between first two terms and last two terms,So: = (x-1) { 2x (x-2) 3(x-2)} Now as you see (x-2) is repeating so we will write it once in a bracket while the other common will also be gathered in other bracket of their own..So, = (x-1) (2x+3) (x-2) (2x+3) is the common we get from both terms, and (x-2) was the repeating bracket that we gathered. This method is actually called Middle-term-break Hope you get it!🙂
The original equation had the first term to the third power, so the answer is minus one less power, so it's to the second power. the 2x^2 is from the 2, the -x^1, or -x is the -1, and therefore the -6x^0, or -6 is the -6.
+Sandra S if u have a factor (x+1) couldn't u just do (x -(-1)) ??? in that way u still have the (x-k) but setting it up that way would give u the positive one...sorry..im a year late DX
I completely understand where your coming from , honestly I have the same problem with all my teachers , but honestly if you think about it , you always have to presume that people already know something otherwise everytime you tried to teach something new to an audience you have no idea what type of people it consists of then each video is going to take an hour ...
i know they're interchangable but it's so annoying that my book will use (x-c), someone else will use (x-c) and then another youtuber will use (x-k) ... rad
You never actually did anything on the Remainder Theorem. You read the description of it, then ignored it the rest of your video... You described the Factor Theorem, demonstrated it with an example, and then went on to even double check it... But you forgot about the Remainder Theorem... NOT HELPFUL!
11 years later this video is saving my butt for online classes
Glad I could help.
which grade are u in?
@@sadafhaddad9415 Grade 1
@@5staryzzz great to know
@@sadafhaddad9415 Lmao
you sorta sound like prince zukko from avatar. It was bugging me this whole time and finally figured it out.
+Cpt Arny OMG YESSSSSSSSSSSS
i hate this because now i can't unhear it
Professor Zuko
Thank you Mr. Anderson. I can't tell you how frustrated I was getting when I was doing my homework using my professor's horrible explanation (which wasn't one at all). You saved my night.
I wish I found your channel years ago. Thank you for what you do. You are amazing🙏❤️
Thank you. Study well.
3:00 What kind of long division is that?I am from India and I have definitely not done something like this and if I do my maths teacher will give me zero.
Edit: I was a lot younger when I wrote this comment. But now after getting into high level Calculus and stuff, I have understood the easiness of this method.
But due to the procedure being beaten in my head, I still find doing full long division quicker because I am at the point I can do it mindlessly.
Aurora Production's I am also Indian and I can relate to you so much.
Saji Antony - True my friend, it is actually called synthetic division but it will never help in gaining marks in CBSE exams.
Aurora Production's
It's synthetic division.
My teacher will give slaps + (-3 marks)😜😜
Remya TG it’s not only Indians. You learn this type of division in the more complex math I think to make it easier
This was great! I have an exam in two days and now I know what I'm doing thank you!!
Maybe drink a little water before you record such a long video next time! Hey, don't strain yourself, alright? Please take care of yourself ^_^ Thank you for the video! I understood it very well
man good job you do alot better than the khan academy dudes it takes me forever to understand them
Glad you found the video helpful. Study well.
@@RandyAnderson hope you are staying well in this time of the virus
@@jeromel4563 I'm doing alright, all things considered. Hope you are, too. Stay safe.
Everybody see that?
My teacher is a good one, but he goes so quickly. This really helped me understand the factor theorem, and what it actually means. I saw the process of doing x-1)(2x^2-x... thank you for making this, you're a good teacher
Thank you. I'm glad to hear you found the video helpful. Study well.
Helpful, but the spit sound in his mouth is driving me crazy XD Just swallow it man.
agree
Ikr
Yes it was freaking annoying as hell (n)
Yaa.......
I think it's just his mic
thank you so much, I'm taking algebra 2 as a freshman in hs and this just saved my butt.
You're welcome. I'm glad you found the video helpful. Study well.
Explained it WAY better than my math teacher did, she gives terrible notes. She moves fast and doesn't explain much. Thank you so very much, you should continue making awesome videos like this one!
Thanks for spending the time on making this video, REALLY HELPFUL
Thank you so much my teacher cannot teach this right and this was so helpful to understanding 🙏
You're welcome. I'm glad you found the video helpful. Study well.
10 years later.... Still helpful for a kid in maths class who don't understand anything
watch less anime then :)
Lol
Randy, please explain to me how to aproach a polynomial when the first 3 terms have powers of 4,3 and 2 respectively, instead of beginning with the cubed term.
its been 3 years but i hope you solved it
If we are dividing by x-1, then the "k" is 1. Thus, the remainder is the same as the value f(1). In the case of this example, f(1)=0, which was the remainder you got after you divided. Make sense?
thank you for explaining it , I read it in text book and kind of got it, but not really. Now after you explained it I can see how they are related.
Now it makes sense!!! Great teaching skills
awesome video. i was able to understand this right away
Great video sir really helped me...🎈❤️
I am glad you found the video helpful. Study well.
Great Video Man!!! Helped me for my exam!
Thank you so much for making this topic understandable!!!
You're welcome. Study well.
you are a life saver. THANK YOU
What happens if one of the coefficients of the polynomial is unknown but they give us the factor of that polynomial? How do we find the unknown coefficient?
Where did your inspiration come from to share your math knowledge with the internet audience? Nice tutorial btw although I don't understand fully the part where you factored . I'll have watch a how to factor video to refresh my memory.
How does this affect when checking if (x-3i) is a factor?
video helped me understand very clearly thank you
why is the value not -1 at 2:03
Hmm... Nothing like my daily dose of ASMR!
Very helpful video nice work!
Sorry but I am to this and i dont understand where you got the numbers from at 3:24, can you explain please?
Thank you! Now I know I can ace my test tomorrow! XD
Scott Disick is that you?
hey thankyou for the vid. im not good at maths could you please explain how you get the quadratic after proving x-1 is a factor. please please i cant fail my maths exam. x
Im crying i cant understand
Bhow f(x)=(x-1)(2x*-x-6) become f(x)=(x-1)(2x+3)(x-2)?i didn't get it ☹️
The quadratic (2x^2 - x - 6) was factored into (2x + 3)(x - 2) in the second line, if you're still wondering. He just used the normal thinking method for that, nothing special.
@arvin Actually it's a bit long procedure which we do in rough portion, So in 2x^2-x-6 , we will multiply the last value which is (6) to the coefficient of first term which is (2) with x^2.. right?
We get '12' , Now we find factors of this 12, So by doing it we get 2×2×3 as factors of 12!
Now you need to have two numbers such that it forms the middle value which '-x' , surely you have to take the highest one number to be negative and the other to be positive, so that our subtraction work is done ✅ and when we get the result it should include (-) sign with it.
So 2×2×3 can be written as 4×3.. ok?
These two values are for the middle term which is (-x), so by writing -4x+3x we will get the same (-x) value!! ..so this is correct.. now we will add this in place of our middle term value, so our expression will be like that:
= (x-1) ( 2x^2 - 4x + 3x - 6)
Now, we will take common between first two terms and last two terms,So:
= (x-1) { 2x (x-2) 3(x-2)}
Now as you see (x-2) is repeating so we will write it once in a bracket while the other common will also be gathered in other bracket of their own..So,
= (x-1) (2x+3) (x-2)
(2x+3) is the common we get from both terms, and (x-2) was the repeating bracket that we gathered.
This method is actually called Middle-term-break
Hope you get it!🙂
How to determine if it is factor by just saying 0??
thank you so much :D the schooling system in spain sucks bad but you've helped a lot
now how do we work backwards when one of the factors is unknown....
aye bruh, how'd you factor all that hooplah?
You have helped me so much!!! Thank you.
You sound like a young instructor . I needed to watch this video again for my Final . Favorited!
I don't get how you got the "2X(squared)-X-6" from?
The original equation had the first term to the third power, so the answer is minus one less power, so it's to the second power. the 2x^2 is from the 2, the -x^1, or -x is the -1, and therefore the -6x^0, or -6 is the -6.
he dropped all the powers by 1, since he divided by "x"
What if the power of x is 4, so how can we factor if we have one divisor.
Now i know how to find other factors. Thanks!
great video thanks, so those zero's are your x-intercepts?
smh
thank you ever so much :) keep it up and help us all with a maths problems :p
Does this method work for a negative factor? like, if you have a factor of (x+1) where x is -1. I tried to do it, but it didn't seem to work. Help!
+Sandra S if u have a factor (x+1) couldn't u just do (x -(-1)) ??? in that way u still have the (x-k) but setting it up that way would give u the positive one...sorry..im a year late DX
can you solve this equation : (8xto the pwer 3 -18xti the power 2 +21x -20) devide (2x-3)
so those zero's are also your x-intercepts
I completely understand where your coming from , honestly I have the same problem with all my teachers , but honestly if you think about it , you always have to presume that people already know something otherwise everytime you tried to teach something new to an audience you have no idea what type of people it consists of then each video is going to take an hour ...
thank you so much for this sir :) helps alot
Hi, this was on my recommended videos, when will I see this in college? Which class i mean
im sure it’s too late now but i guess no response in nine years is your answer
I love you dude
You are simply amazing!
Thank you so much you help me for my test
i know they're interchangable but it's so annoying that my book will use (x-c), someone else will use (x-c) and then another youtuber will use (x-k) ... rad
Thank You so much... Helped me a lot!
Thanks! Was looking for this for a long time, phew
awesome. went to lecture class. picked up one or two things. this video, i have it locked
Where did 2 -1 -6 come from plz tell me
He added the values above them in the synthetic division table.
you have a nice friendly voice
im fucking sobbing at 4am. i need to pass this worksheet or else i wont be able to take the exam later.
Loved it.
1/6 = (-6) ? Why? Isnt suppose to be 1/6=(+6)
You are awesome!!
Thank you. I'm glad you found the video helpful. Study well.
THANKS. THAT HELPED
Firelord zuko why are you doing math
Thank you!!!
Good job! Couldn't get that from my textbook :D
How did the test go
@@lemonlime8949 bro now I think he has children
@@Ahmad-if9ro bahahahah righttt
U saved my life, thank u so much
Thanks, this helped a lot
Please tell me 2 -1 -6 how happened this
he used synthetic division.
Your dribble is distracting but the video was helpful! Thanks!
bruh, I can just add them up like that?
When doing synthetic division, yes. See: ua-cam.com/video/HzhNQ8a9rls/v-deo.html
I love it!
Great video. Thank you!
nice!! Luv it so much
should buy a voice muffler thingy to cut out unnecessary mouth sounds.
Thanks, really helpful.
You are the best
Awesome video! :))
@EllipticalExistence Your comment made me LOL.
life saver
Great vid . thanks
well explained!
Thanks
Thank you, sir
You never actually did anything on the Remainder Theorem. You read the description of it, then ignored it the rest of your video... You described the Factor Theorem, demonstrated it with an example, and then went on to even double check it... But you forgot about the Remainder Theorem... NOT HELPFUL!
Prince Zuko?
THANK YOU SO MUCH!
thank you so much!!
Explained this way better than my maths teacher.
They should introduce a love button
F (x)=this video was helpful
my equation is x4-3x3 + x2+x+4
honestly they should take all the online teachers and put them in class rooms instead of having horrible teachers
Good vid