Remainder Theorem and Synthetic Division of Polynomials

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Remainder Theorem and Synthetic Division of Polynomials

Рет қаралды 915,244

Күн бұрын

This precalculus video tutorial provides a basic introduction into the remainder theorem and how to apply it using the synthetic division of polynomials. It explains how to evaluate a function using synthetic division. The value of the function is equal to the remainder when f(x) is divided by a linear factor. This video contains plenty of examples and practice problems on the remainder theorem and synthetic division.
Introduction to Polynomials:
• Polynomials - Classify...
Polynomials - Basic Operations:
• Polynomials - Adding, ...
Dividing Polynomials By Monomials:
• Dividing Polynomials B...
How To Graph Polynomial Functions:
• How To Graph Polynomia...
Intermediate Value Theorem:
• Intermediate Value The...
_____________________________________
Long Division - Polynomials:
• Long Division With Pol...
Polynomial Long Division - More Examples:
• Polynomials - Long Di...
Synthetic Division of Polynomials:
• Synthetic Division of ...
Remainder Theorem & Synthetic Division:
• Remainder Theorem and ...
Factor Theorem & Synthetic Division:
• Factor Theorem and Syn...
Rational Zero Theorem:
• Finding All Zeros of a...
______________________________________
Real & Imaginary Solutions - Polynomials:
• How To Find The Real &...
Solving Polynomial Equations - Synthetic D:
• Solving Polynomial Equ...
Solving Polynomial Equations With Excel:
• Solving Polynomial Equ...
Writing Polynomial Functions Given Zeros:
• Writing Polynomial Fun...
Descartes Rule of Signs:
• Descartes Rule of Signs
Solving Polynomial Inequalities:
• Solving Polynomial Ine...
_____________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 411

@TheOrganicChemistryTutor Жыл бұрын

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzfaq.info/get/bejne/eJmSisWg08WZh40.html

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@user-mr3wf3xy4t 4 жыл бұрын

I'm just advance studying since I'm being grade 10 next school year, and it was said that this was one of their lessons. I tried to make fun of the equations and made my own equations and still, f(c) and tbe remainder is ALWAYS the same, which I was so amazed how accurate this theorem is. Thanks!

@jbwoy5615 3 жыл бұрын

How does he take 0 as a coefficient of X?

@krislegends 3 жыл бұрын

@@jbwoy5615 because all terms of an equation has a power, from lowest to highest. Then if one term is missing, then the variable of that power must have a coefficient of 0, which when multiplied by zero equals zero. In math, anything equal to zero is not included.

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@jackwilson7018 5 жыл бұрын

Wait the original expression had, - 12, not 12

@raid2654 5 жыл бұрын

I might be late but it became postive because +24 - 12 is +12

@ohsweetea 4 жыл бұрын

@@raid2654 he meant the original expression. it was positive 12.

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Wait he did correct that at 3:20

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@blep295 3 жыл бұрын

hi idk if u can see this but at 8:33 they added two zeros and I'm lost can u please explain why they added the two zeros even though it had x^2/xsquired since they explained at 5:15 we add zero because it doesn't have x^2/xsquired

@ssinistershorts 3 жыл бұрын

@@blep295 heyy idk if you still need help but imma help you, alright so the equation has 2x^4 and then 3x^2 then 30 which has no x, in such situations you have to add numbers to replace the missing power, in this case it a number with a power of 3 and a power of 1. when u add the non existing powers you always have to add them as 0x^n where 0 is constant and n is the power missing. if the equation had a number with the power of 5 but no number with the power of 4 then you will have to add 0x^4. so the equation in the end (the one in the video) would look like: 2x^4 + 0x^3 - 3x^2 - 0x + 30 (notice that you dont write the number 1 when the number is to the power of 1) hope this explained c: if you still need help you can reply and ill be sure to help you.

@Renjoku Жыл бұрын

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@georgesadler7830 2 жыл бұрын

MR. Organic Chemistry Tutor, thank you for analyzing and explaining the Remainder Theorem and Synthetic Division of Polynomials. These are useful tools in all levels of science and engineering.

@CHRF-55457 11 ай бұрын

wow... wasnt expecting to understand the Fact Remainder Theorem within 3 minutes of watching this video... your a life saver.

@Multi-stan_girly 8 ай бұрын

Exactly 💯😮

@Giankurl 7 ай бұрын

At first, the concept of remainder theorem was very complicated for me, but through this help full tutorial, I managed to understand it better. thank you very much

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@user-gp2sf7kx2g 7 ай бұрын

Thank you, I now understand the remainder theorem and synthetic division of polynomials.

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Wow, just watched this video and I clearly understood the concept. What my lecturer tried explaining in hours, confusing himself and we, this man just taught it well in less than 11 min 🔥👏👏

@zeenatkazi721 3 жыл бұрын

I never knew it was this easy ! Thank you for making us understand :)

@user-yy3xd4vl8s 2 жыл бұрын

On the second question why did they add zero

@lexipalmieri7358 2 жыл бұрын

@@user-yy3xd4vl8s because the exponents need to go in descending order for synthetic (and long division w/ polynomials) to work. I can’t remember example 2, but another example would be 3x^4 - 2x^2 + 4x - 5. There is no x^3 in that polynomial, but technically there is a 0x^3 (since zero times anything is zero, it doesn’t change its value) so you would just put a 0 in between the 3 and -2 (in this random example I made up) when dividing. Hope this helped

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@Multi-stan_girly 8 ай бұрын

Thansk for this info . My lecturer was making remainder Theorem so complicated

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At 2:57, in the synthetic division it was supposed to be -12 not 12

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In the last equation you should also add another 0 for the coefficient of x because it is missing in the equation

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@timothymattnew Жыл бұрын

This statement of the theorem is incorrect. The actual theorem states that, given a polynomial P, for any number c there exists a polynomial Q such that the identity P(x) = (x-c)•Q(x) + P(c) is true for all x. It sounds a little bit more complicated than presented in the video, but it's ACTUALLY correct, and you'll never secondguess your reasoning if you use the correct version of this theorem after understanding the not-so-complicated proof on its wiki page (I advice you guys to read a little bit on the theory of polynomials as well). This result is especially powerful because it states that Q is a polynomial, which can be used in a countless number of ways and contexts, including linear algebra, abstract algebra, number theory, probability theory, mathematical optimization, real analysis, etc.. There is a nice article on polynomial remainder theorem in Wikipedia, I actually like how straightforward the second proof listed on this article is.