Most math teachers just teach math as a set of steps/processes. They don't actually teach the mathematical logic/concepts behind what students are learning. When students lack foundational knowledge, they aren't able to figure out these things on their own. As for Synthetic Division, I don't care for it, I would rather use an area model or long polynomial division -- things I actually understand.
I sometimes struggle to remember how to properly use ruffini's rule without getting something wrong - I think the "cubo di binomio" (a+b)³=(a³+3a²b+3ab²+b³) would have been easier to do here on the numerator
I am from Italy, and calling it the ruffini rule instead of division is already a mistake as you can t grasp the concept properly, plus they never teach you to divide for and x-a where a is not a solution which sometimes can be usefull as well
I want to thank you! This is the quickest and simplest way this has been explained. I've gone through so many 10 minute videos that are extremely confusing. Your video is the only one I actually understood and was by far the shortest. Again, Thank You so much!
Thank you Master! These shorts are really productive , time saving and cool at the same time for someone like me in their learning phase and preparing for competitive exams And I really appreciate the efforts you put into this. Please continue your work
Love these! Before it’s all over, I am going to formally enroll and complete all the mathematics I struggled with as a young person. This is so inspiring and enlightening. Thank you for producing these shorts, please keep it up!
A concept that I thought would be hard to relearn after months of not touching it was reexplained to me in less than a minute. Thank you for your great work.
Our calculus professor came to us one day all excited because he had just learned synthetic division and he wanted to show us all for partial fraction decomp for Taylor Series. The whole class was wow'ed by something so simple.
It's actually called the Horner method 😊. Very useful for factoring. In general, a good way to get the first root of the polynomial is to search an "evident root" . Here it was 3, so we were able to proceed with Horner's method.
Don’t worry, I’ve gotten A’s in multiple Calc classes and literally study math for fun, but I CAN NOT do synthetic division… something about it just breaks my mind
@@Emily-fm7pt Don't worry, I had to use the normal method to see why this works. I don't get why you would go through the effort of memorising this algorithm and take the risk of missing an exception, instead of just performing the normal polynomial division...
@@Emily-fm7pt when you divide a polinomial by one of its roots, the resultant polinimial is one of leaser degree, because the polinomial higher degree show the ammount of roots the polinomal have (real and/or imaginary roots)
I’ve been trying to find this type of video for a while bc idk how to get the final answer of my problem but now I do!, Thanks so much (your a lifesaver!)
This is amazing; even though I don’t know why x-3 can be zero, especially it is a denominator; I was taught the denominator cannot be a zero, yet it is so cool to learn a new way like this. In the past I just thought it would be like (x-3)^3, so the answer is (x-3)^2.
pareil dénominateur =0 interdit de plus ne comprenant pas l'anglais et ne pouvant pas traduire les sous titre sur les "short" ...ne ne comprend strictement rien a ce qu'il veut démontrer
I have been wanting to ask this for a long time ever since i was in 7th grade, it was about a math problem that was shown in this clip. It was at this moment i came across the same problem that i was curious about back in 7th grade, now that i watched the clip over and over again, i can finally say i dont understand shit.
@@manjulasingh5669 He deliberately gave an example that would come out evenly with no remainder. And in fact, this example is a perfect cube, where your method would work. It ultimately reduces to (x - 3)^3. In general, it wouldn't always work that way, even if you were given a denominator that divided with no remainder.
The last time I needed to do this was an exam in algebra 2 back in high school. I have since taken a boatload of college level math courses, and if you ever ask me to divide a polynomial, I'm gonna whip out MATLAB. Such a useless skill to learn.
I had several classes in calculus .This is the first time I ever saw this .I am like what the hell ? I absolutely don’t t Remember doing that in Algebra 2 or in College Algebra
Well there are other polynomials that can't be fully answered by the synthetic division and can be answered fully by the long division, and this thing barred me from using synthetic division and force me to use the pain in the ass long division and this happen multiple times.
Can you please teach us a way to remember statistics, of standard deviation, linear regression and confidential interval. As I found it somewhat hard in school
haha my ap stat exam is tomorrow! the one thing i would say is lots of memorization. for linear regression you would need to know how to read computer output and interpret a variety of things. why do u ask? are u taking a college stats class?
But you need to notice that the numerator is (x-3)³. If you don't notice that, you won't be able to solve it this way The method shown in the video works for more examples, where you can't use short multiplication formulas
i have another method. club the x^3-27 together and apply the identity a^3-b^3=(a-b)(a^2+ab+b^2) and from the -9x^2+27x , take out -9 common, in the end (x-3) as a whole can be factored and the remaining term is the answer!
@@useless1026 no it isnt? it's literally like a two step solution. If you have an idea of these identities and how to parse complex algebraic expressions, it would take you no more than 5 seconds to perform what i just described.
What is the reason why we solve for the value of x in the denomitor to be use as the divisor in synthetic division? What is the logical reason for that?
If schools were FACTORIES, and children were ROBOTS, and intellectual understanding was a technical algorithm of ACTIONS... then this explanation would be excellent!!! Tamir Erez Math teacher.
I'm not sure what grade math you teach but I'm thinking you're an advocate for the common core math. Different educators have different ideas on how to teach math. I won't say which method is better but everyone is entitled to their opinion.
@@mrhtutoring I taught math in highschool, grades 11-12 before matriculation exams, I was an instructor for psychometric tests and a chess instructor. What you did in the video was simply to solve the problem. You solved it very well!! But in no way did you teach HOW to solve and WHY. I see more of your videos, and you are an excellent teacher, but in this video we saw "someone" who knows how to solve, and he did, in fact, solve. But in no way did we learn to solve by ourselves. no way! Maybe it's because you put yourself in the narrow format of "shorts" Which allows you to solve quickly, technically only, without explanations. Other than that, thanks for a good math channel.
@@mrhtutoring I love your style because it takes something I already know and shows a new way or a different approach or shows me a forgotten approach 😋❤ love from germany
