You should always do something with teaching I hope the school you work for is giving you an incentive or added benefit cause you’re an incredible teacher
Great examples and I love to see this idea because I always say you can't do synthetic division when dividing a quadratic. It is awesome to see a way around that.
I usually just focus on long division but think it is important for students to understand why, hopefully with this video they seee the point of learning long division haha
@@brianmclogan True, long division would be faster because you are not repeating the process twice or dealing with multiplying the complex numbers or root expressions.
Reducing problem to linear factors force us to use complex numbers but there is modification which avoids complex numbers I used it for my implementation of Bairstow's method
@@brianmclogan b_{n} = a_{n} b_{n-1} = a_{n-1}+u*b_{n} for k = n-2 to 0 step -1 do b_{k} = a_{k}+u*b_{k+1}+v*b_{k+2} enddo (In Bairstow method we create two sequences using this version of Horner's rule , then we solve 2x2 system of linear equations with Jacobi matrix Bairstow method uses Newton's method and there may be problems with convergence or with choosing good initial guess)
But what if you have a remainder when synthetically dividing by the first factor of the quadratic? How do you transfer that to the second division if at all?
@@letstrywindows8986there’s a video called something like “synthetic division by a quadratic factor” by a RU-vidr called “math and stats help”. That video teaches a more advanced way to do synthetic division for such a situation. But the bottom line is that the traditional “quick and easy” method of synthetic division does not work when you have a remainder after the first round.
I don't understand when you are supposed to repeat synthetic division when it doesn't work. I saw that my teacher divided by -1 in synthetic division, got a remainder, so my teacher divided it by -1 again. It's one of the things that bugs me. When do I stop attempting and move on to the next possible divisor? Thanks!
Your teacher made a mistake. You are not allowed to synthetically divide twice using the traditional method if you have a remainder after the first round. There is a more advanced method to do that, or you could do long division.
It actually is -2i^2 but he simplifies it because I= sqrt of -1, I^2 is just -1 because squaring the sqrt of -1 just leaves -1. The expression now becomes (-2)(-1) which is 2.
I like your research 😉. It was wow. Above that, l plead with you that you should reconsider a pen to use. The orange ink is invisible. Don't use it. Thanks
