Finding ALL Solutions of Polynomials (Precalculus - College Algebra 37)

How to completely factor a polynomial over the complex number system and find all of the solutions, including complex.

[wrgzgru]

I can't thank you more Professor Leonard, I just passed my calculus 2 exam theory because of you and i almost got 100% on it. You are the best, keep it up and thank you for your videos. Joining you on Patreon very soon!

[harrygolde]

When are you going to teach us your workout routine??

[hjkjy]

Professor Leonard, you are my biggest inspiration in life, buff and smart!

[mejolic]

Lots of love from India. Sir. M in love with ur teaching techniques.

[IdontKnow-gmeu]

You're a terrific teacher, thanks for all the help and for the free material.

[scopeless]

On thing to help too is if you have positive descartes values, all the signs on the exponents are positive, and 1 is too high, you don't need to try any higher values so only the fractions can work. Same for the revers if 1 is too low then only higher numbers can work and the fractions wont.

[akwesiappiah]

Waiting patiently for trigonometry!
Those who watch this channel often any good channel to learn trigonometry in full.

[georgesadler]

Professor Leonard, thank you for an exceptional video/lecture on Finding All Real and Complex Solutions of Polynomials. Factoring and Synthetic Division continue to play an important role in finding real and complex solutions.

[OctoberMorningRain]

Honestly thank god for you. There's no way I'd be able to understand this by reading from a textbook.

[veryhealthy]

20:30 onwards

Holy...shit. So that is why its called LONG division!

[simplyjenny]

Please do some more differential equations videos

[hamzahashim]

How do we interpret complex roots of a non-quadratic polynomial graphically?

[ariabakhtiar]

Please make a Delta-Epsilon definition of limit

[samipickard]

"because what i is is imaginary" 😂

[benye]

Hi Professor, love your video and a big fan of your channel. I ran into a problem which need your help to shed some lights on it. For polynomial y=x^{4}+22x^{2}+50x-25, Desmos graph calculator shows it has 1 negative (-2.255, 0) and 1 positive (0.421, 0) and 2 imaginary solutions, but rational number solutions are not the factor of p/q 25/1 (plus minus, 1, 5, 25 etc.), is there a reason why rational zeros theorem does not work for this polynomial?

[franciseylim]

I come here to click like first (as working in the morning), later at night will watch this video.

[bethcox]

You can use synthetic division with complex numbers. Is there an advantage of not doing it that way?

[saljimenez]

Professor Leonard, I have a question about Descartes's rule of signs. If you run f(x) for the equation it says that we will either have 3 or 1 positive x-int. And if you run f(-x) for it then you have 1 negative x int. Am I correct or is there something that I am not looking at?

[scopeless]

Ive been watching these at 1.75 speed and just realized that now I'm used to his faster higher pitch voice and his normal voice sounds weird.

[HritikJain]

Can you make something on pure mathematics? It would be just great😍