Solving Higher Order Polynomials Pt 1 Rational Zeros Descartes Rule

In a 2 part video I show you how to solve equations with a degree larger than 2 without the aid of a graphing calculator or computer.

[Peepummms]

If anyone wants a typed out version of the notes:

Steps for solving higher order equations
1. List all possible rational zeros
-(+-)factors of constant
-factors of leading coefficient
2. Use Decartes Rule to try to limit guess and checking.
- Number of positive real zeros = number of sign changes, or reduced by multiple of two in f(x)
-Number of negative real zeroes= number of sign changes, or reduced by multiple of two in f(-x)
3. Use synthetic division of possible rational zeroes until you geta remainder of zero.
4. If remaining factor has a degree >2, keep using synthetic division to break equation down. If degree equals 2, finish solving with factoring or quadratic formula.

[profrobbob]

OMGoodness....what a testimonial! Thank you for making me your "go to" youtube teacher and I wish you the best in acquiring that engineering degree.

[profrobbob]

Very observant...shows me that you are REALLY paying attention to my posting! You'd fit in just right in my classroom:)

[profrobbob]

Yes....and you will have to repeat the process until you get down to a degree of two. This unless you notice that some factoring skills will help you solve this problem much quicker. A few steps of factoring and you will be almost done.

[profrobbob]

I am thrilled you like my videos:D Thank you for watching.

[syedaa]

All your videos are so helpful, thank you for explaining so well. I've used them to study for every precalc exam this semester so far.

[georgesadler]

Professor RobBob, thank you for another powerful video/lecture on Solving Higher Order Polynomials Part One by finding the Rational Zeroes and using Descartes Rule to find solutions. Graphing calculators are also helpful for finding solutions for higher order Polynomials.

[ThuyNguyen-buge]

I think in order to create those graphing calculators, the programmers had to truly understand how to solve polynomials; these methods that we're learning are key.

[maxbresticker]

Instead of using synthetic division to check your potential zeros, couldn't you use the remainder theorem and just plug in the possible zeros till you get like f(-3)=0, where you know -3 is a solution?

[alyssahaack]

at the time 8 :25 in the video isn't the -3x squared supposed to be positive 3x squared

[annmcb]

Thank you!  I am always grateful for the extra help from your videos.

[cecoleman]

how do we check these using a graphing calculator, to save time?

[CrohnieCommunity]

if for say we get x^5 + 2x^4 - x -2 do we also solve this using long div and the same sort of process as cubics?
btw ur vid are AWSOME!!!!

[HaleyKinsler]

When you plugged in the negative X for Decartes' rule of signs, wouldn't it have been -x^3+3x^2+13x+15? The -3 times the -X^2 should have ended up with a positive number, I believe, but I thought I may as well comment and check.

Also, when you say that you'd have to do synthetic division again if the equation is of a degree of four or more, how exactly does that work? Do you simply take your possible roots from the rational root theorem and test them again? Or, do you divide by the same number you used the first time you used synthetic division? Thanks!

[THEQuantumPolkaDots]

Maybe I'm just missing it, or even completely misunderstanding something, but do you have a video explaining the upper and lower bounds, like for when you have a lot of possible zeros and you don't want to guess through them all?

[mathcruz]

Do you have any videos that go over solving polynomial equations by factoring? 

[motherofpearls]

Lol, you got one question done! 😂 btw, I understand how you got the -3 and 1, but please explain how you got the 5. Thank you.

[maxchillin]

I could be wrong but at 11:35 I think it should have been positive 5 instead of negative 5 but I could be wrong.

[ahbabmurtoza]

Please don't mind +ProfRobBob; I'd like to know that shouldn't the last three answers be -3, 4, 1 instead of -3, 5, 1 because 6+4 is 8 and 8/2 is 4? Please kindly tell me am I thinking it the right way?

[tb]

Why does Descartes's rule of signs actually work, though? It just seems like magic to me at this point/doesn't make intuitive sense. Kind of hard to find a proof that a high schooler could understand.