Polynomial remainder theorem proof | Polynomial and rational functions | Algebra II | Khan Academy
Вставка
- Опубліковано 24 лис 2014
- Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacademy.org/math/alge...
Watch the next lesson: www.khanacademy.org/math/alge...
Missed the previous lesson?
www.khanacademy.org/math/alge...
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
/ channel
Subscribe to Khan Academy: ua-cam.com/users/subscription_...
Well that's easy to understand. So many books and videos and lectures just say "here's the theorem, do it, it's magic." It's frustrating, but the proof turned out to be really simple and now I know how it works, and now I'll remember it.
Exactly my dude
exactly, so few sources actually care to explain the how, the why, but thats how i remember, through understanding it deeply
is this guy is a god or scientist he knows everything.... everything from history to science from geography to English
I think khan academy is not one person, but rather write a few people, though they would all be very knowledgeable, of course
I love learning Sal's "Khancepts".
It's one thing to memorize these formulas, but it's so much more easy to recall when you have the gist of how they work on this level. Thank you for sharing!
After seeing this proof, I lost respect for the polynomial remainder theorem
Thanks Sal, I was having so much trouble with the remainder and factor theorem. Now i have got a good understanding of the topic .
My math teacher didn’t want to explain this to me. I have no idea why, but this video saved me so thank you so much
The math teacher probably doesn't know themselved
Thank you sir, it was really helpful.
Wow, that was interesting!
Excellent handwrite
U are a genius thank u.
Love ur vids
❤
Great video!
Marvelous and extraordinary
Thx sir
.
..
This gave me great satisfaction....
I asked it to my teacher too but she fail to make me understand ..u helped me ..great job
Perfect way to proofs
How can f(x) be written as f(a)?
We put a into the function.
since the functions f (x) and the Right hand part are equal, we should be allowed to put any value of x. So we put x=a
Thank you 😊😊🌟
Thx Sal. Never learned this in math so it was really useful cuz I'm tutoring kids now
Good learn and teach
I was randomly watching this video for a long multiple-layered question (if you know what I mean) when it suddenly hit me.
Under the right conditions polynomials can describe any number in any numbering system [Decimal, Binary, Octal, Hexadecimal]
Is this just to prove that as long as you have x-a you can get remainder in a short period of time? Assuming x is equivalent to the a and therefore arriving at a y coordinate
satisfaction
Hello everyone, does anyone know where the next video is, the link he gave may be wrong, I don’t think it is continuing this video.
proofs are always satisfying
Why dont they teach this in school..or why isnt it something people naturally conclude or deduce on their own..I dont think even ramanujan wouldve thought of this hinself had he not aeen it..also you dont need to use it that often...
Oh god thank you so much !!!
Sal this is a great video and taught me a lot, but one thing you forgot to mention is that x=a
Actually, the generalisation isn’t (x-a), it’s (ax-b), and the remainder is f[-(b/a)]
Alas! Sorry to say
I understand most of your proof(how does the stuff work)videos
but couldn't understand this one
im guessing u got confused at the part where they wrote f(x)=f(a), right?
To fully understand this you have to understand the division algorithm theorem
when I divide a constant by 0 why do I get the dividend as the remainder
can someone please tell me how did they write f(x)=f(a)? like what
sir what do you use for writing???
Did you come to know? I wanna know too.
I love proofs
Anteater23 me too
me three
Me four
Me five
Me six
I liked is British accent so much
Meant 6*(4 +1/6) = 25
1st!!!!
I have a doubt about the proof, if 'q(x) is ( f(x) / (x-a) ) - r' and 'x=a', it's gonna include a division operation by 0, what do mathematicians say about this problem?
q(x) = f(x) / 0 - r
Anyways Sal's lessons are always so satisfactory to me-almost always, the 240p videos are a bit odd-. I really appreciate Khan Academy's free lessons on mathematics. it's free but the satisfaction is great. I mean I didn't feel much interest in mathematics when I was very young, I wish I had had this kind of self education system when I was a student haha
math.stackexchange.com/questions/2768747/polynomial-remainder-theorem-seems-to-use-divide-by-zero
hes a simple guy thats it
what if the divisor is x+a are we still gonna are we still gonna take f (a)
No you gotta change it to f(-a)
the original is x - a right?
then how did x - a got to x + a?
well, the only way is
x - (-a)
if a is a negative number say, -3 then x - (-3) becomes x + 3
if it is a positive number say, 3 then x - (3) = x - 3
In which class do u study this in ur country????
For me grade 11
??
U essentially converted the divisor into zero
How's that possible
just by substing the constant A in that place of X..like of try substuing f(1) on place of A..we'll get same as the proof which is in the previous video.
yeah, it doesn't make any sese logically like how can you divide by 0 that's not defined - have you come across any other derivation that makes more sense without breaking that rule (the rule being that the divisor can never be 0 )
Haha easy right
*sees proof*
What is this witchcraft.
This therom says if we devide by (0) to something the reminder is always equal to the devident....
x-a
=1-1
=0
x=a