Synthetic Division and Remainder Theorem
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- Опубликовано: 12 июл 2023
- Comparing dividing polynomials using long division and synthetic division.
The lesson includes synthetic division with and without a remainder.
Synthetic division is most useful when finding the value of function using the remainder theorem.
Who wants this man to be his high school teacher.
I had a really great math teacher during my junior year of high school, he taught me this & I loved math then.
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Screw that, I want him in grad school
I would gladly have him as my math teacher. His explanations are simple and clear. his writing on the other hand only gets a grade of C.
I was never taught synthetic division. This was great. A good way to double check your work.
It only works when x is to the first power.
@@chocolateangel8743 Yeaaaaaahh! :-)
THANKS Mr. H. ,I am an old student of 66 years and you give new methods for win time .
You sir are a gift to humanity.
agreed
I remember learning both long division and kind of synthetic Division methods as well as remainder theorem in my 9th standard.. but I never applied it this way.. it always worth giving time to your videos.. I revised as well as learnt such a surreal application. Wholeheartedly thank giving to you sir for uploading it on RUclips and connecting with us.. may God help you achieve your summit..😊
Sir Good Morning 🙏
You are Unique in your Math Teaching....
Almighty Bless You Sir
You have a fantastic ability to make what initially looks like a difficult problem into an easily solvable one. I wish all mathematics teachers that I ever had would have broken it down so easily and quickly. Thank you.
Thank you very much!
Thank you Mr. H as always, it's always a pleasure to listen to your lectures 😊
So nice of you. Thank you!
First thing first - I zoom in to Mr H's videos and gain a wealth of knowledge. Math stablizes -- making me a fervent admire of your lessons.
Excelent video, it covers all posibilities. Thanks professor!
Thank you for the review, it is always good to go over useful methods.
That was very clear and didactic, excellent material, thanks.
Glad you enjoyed it!
Some people will say you cannot do synthetic if the denominator is like 2x + 1 or 3x - 5, but you can. You will have a fraction on the outside and have to divide your final answer (except the remainder) by the denominator of the fraction.
Never seen Synthetic division ever. This looks lot more fun
Absolutely beautiful and easy to understand. What a great teacher you are..
Thanks so much 😊
Thank you Mr. H
Thank you very much for your videos. I will try to support your channel so that it reaches more people, those people who teach and enjoy it are greatly appreciated, especially when it comes to mathematics. Thanks again
You're just superb dear Sir. You make these explanations so simple to understand. Way to go .. keep going string....
This was the coolest thing ive seen in a long time. I love Math!
Thanks. Always reviewing the basics.
You are legit the best professor in the whole youtube
Magnificent, not words...Love you
This is polynomial made easy.Much love from Nigeria
Amazing ‼Thank you professor 👍🏻
Thank you very much, I love your instruction
You have fantastic teaching skills😊🎉
Outstandingly concise. Enormously helpful. Many thanks.
You're welcome!
So, so helpful. So specific.
I learned synthetic division in university, but we call it Horner's Method. It's so convinient.
Thanks for an excellent presentation.
Thank you so much Sir. Your videos really helps a lot. 🙏🙏🙏
Thank you Mr. H, this video is amazing, cleared all my concepts regarding division of polynomials!
Glad it helped!
Thank you Sir!Nicely done!👍
Clear and excellent explanation
Hello Mr. H. I just found your channel and subscribed immediately. Your teaching methodologies are superb!
Welcome aboard! And thank you! 😊
This teacher deserves more views and credit in teaching us math
Thanks, I appreciate it.
Excellent tutorial staff
You are amazing teacher God bless❤❤❤
Well done!, thank you.
You should teach math teachers how to teach because you're an amazing teacher....
Love it .Did this years ago
How wonderful. It's easy to understand the explanation.....Thank you
Glad it was helpful!
Liked👍 sir
I remember doing synthetic division back in HS! Fun times!
Thank you for this fun explanation!
Glad you enjoyed it!
The long polynomial division method is good for those that view division as repeated subtraction. However, for those of us that view division through the lens of multiplication, an area model might be easier to understand. I would encourage you to through up a video on that, when you have the time. Oh, it's also faster than long division, works all the time, and takes up less space. Since I have a preference for it, I don't care for synthetic division (or how it's typically taught).
Thanks professor
Wow you're such a wonderful teacher
Wow, thank you!
Nice!
great thank you
First time i heard it and it gonna save lot of time 😆
❤❤❤🎉🎉🎉 Excellent
Here is a traditional polynomial division.
x³+3x²-4x-12 : x-2 = x²+5x+6
x³-2x²
------
5x²- 4x
5x²-10x
---------
6x-12
6x-12
-------
0
Best regards
Marcus 😎
Thank you sir for explaining us in such a beautiful way . I hope I pass tomorrow ❤
All the best
@@mrhtutoring thank u sir ❤️
I am learning a lot that will be useful in my own teaching from this wonderful teacher
A common mistake that one makes, when not in class, is because we miss out on the rules by not being in class when we are supposed to be . I see that now but it is never too late for miss lessons.
Great!
Thanks you sir
Thankyou.
very good explanaition, thanks
Glad you liked it
Great video, clear and straight to the point. I cringe at the chalk sound though, if you could use a whiteboard instead it would be better :)
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If you have a quadratic in the denominator, could you factor out both of the linear factors, and then use both values of x (if multiple) as the dividend (for the synthetic division)?
Nice
Ok sir.
I wish Mr. H is my tutor
👍
I am Indian but I watch this video to understand some concepts.
Sir please help me to find this
Integration of tanx under root dx
Sir please can you teach polynomial graphs
It is the most easy math ever
For remainder theorem what about e.g. P(-1)?
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What if the p(5) was negative, like p(-5)
I love the long division! I'm not so sure about the synthetic division though. What if the denominator in the first example is something like 2x^2-10x+4=0? Long division still works then, but synthetic division will return 2 solutions for the denominator. In fact, what if the denominator only has complex solutions, like 2x^2-3x+4?
Synthetic division only works when the divisor is power of 1
Synthetic division still works when you have no real solutions. You would need to appeal to complex numbers to find your component polynomials. It's much easier to use polynomial long division, any time you don't have a real root to work with.
Consider the example of:
x^4 - 2 x^3 + 6 x^2 - 2 x + 5
which has no real solutions, but has a known factor of (x^2 + 1).
This means two of its complex solutions are x = i and x = -i,
Synthetic division with x = i as one root, pens out as follows:
i |_1__-2______6_______-2_______5__
. .______i_____-1-2*i____2+5*i___-5__
. . . 1 . -2+i . . 5-2*i . . . . 5*i . . . 0
Continue the same process, using x = -i.
-i |__1___-2+i____5-2*i____5*i___
. . _______-i______2*i______-5*i___
. . . . 1 . . -2 . . . . 5 . . . . . . 0
Resulting factored form:
(x^2 - 2*x + 5)*(x^2 + 1)
Sir I really like the way you teach. Sir have you qualified SAT. And pls tell about the level of english in SAT (easy, moderate , tough)
It's quite tough.
If you have any idea about Indian SOF english olympiad pls compare it with SAT and tell the level
Excellent technique
I like your way of explaining.
In the first division, you didn't have a close parenthesis for the expressions being subtracted.
Make a video of how do you study math pls.
X^3+3x^2-4x-12=x^3-2x^2+5x^2-10x+6x-12=(x-2)(x^2+5x+6).thus quotient is:x^2+5x+6.ans
My high school math teacher was horrible. I had to learn most of my math in college. Assuming that you can rock calculus like you can algebra I would have been a lot better off.
I second (H) and (B)
I have never been taught this synthetic division, need more practice to get familiar with
It's quite helpful.
Much quicker and efficient than the long division method.
This is good stuff, however, I really need to see how this is done with a calculator. Just being real. I wish I would have had you in juniorhigh when I got hopelessly lost in arithmetic .
Why is it a 5x³ and not an x³, If you are subtracting 3x³ from 2x³?
+3 - 2= 5?
My solution, without watching the video or reading other comments. 😎
(x³ + 3x² - 4x -12) : (x - 2)
DIV 3 2 1 0
‐---------------------------------------------
2 1 3 -4 -12
2 10 12
-----------------------
1 5 6 0
Solution
x² + 5x + 6
A requirement is a divisor of the form (x + a) with a ∈ ℝ.
Best regards
Marcus 😎
great video, tho in 8:08 you put theorm instead of theorem
Thank you for pointing it out. I missed that one.
Beautiful and simple proof 🤩
Let P(x) be a polynomial of degree n
To perform the division of P(x) by (x - a), we use the method of polynomial division. Let q(x) be the quotient (polynomial of degree n-1) and r be the remainder of this division:
P(x) = q(x) * (x - a) + r
Now, let's evaluate this equation at x = a:
P(a) = q(a) * (a - a) + r
Since (a - a) is equal to zero, we get:
P(a) = r
In India we learn this technique in 9th standard😊😊
So?
Why mr caste
5:06 you mean x² not 1x²
They both mean the same thing. x^2 implicitly means 1x^2.
great synthetic division is great but Pakistan kay jahi teacher is ko wrong ker Daitya hain like in KIPS school soan garden ISD.
Long division is better.
I was NEVER taught this in highschool, now I am mad.
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