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

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Professor Leonard Merch: professor-leon...
How to completely factor a polynomial over the complex number system and find all of the solutions, including complex.

[@user-wr9gz1gr3u]

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!

[@hjkjy4602]

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

[@malcolmjelani3588]

🤫

[@harrygolde6031]

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

[@mejolic]

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

[@IdontKnow-gm7eu]

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

[@georgesadler7830]

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.

Thanks for the lessons, sir.

[@angajasonr.2422]

Thank you sir.

[@akwesiappiah1571]

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

[@Manny24_8]

there are no good channels for trig unfortunately. I also am waiting on prof Leonard haha

[@kadarfrisby7991]

This is very helpful, thanks!

[@scopeless22]

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.

[@Tiwari1_9]

Thanks

[@KingKakashi45]

you are the BEST

[@simplyjenny7918]

Please do some more differential equations videos

[@veryhealthy9962]

20:30 onwards Holy...shit. So that is why its called LONG division!

[@charlottelessels7901]

love you

[@samipickard589]

"because what i is is imaginary" 😂

[@ariabakhtiar7998]

Please make a Delta-Epsilon definition of limit

[@somasahu1234]

Yeah I also want it...

[@franciseylim11]

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

[@hamzahashim4741]

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

[@benye4040]

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?

[@HimuraK1]

Professor Leonard mentioned two videos ago that Descartes’s rule may not supply all the multiples, especially when you use the quadratic formula to factor. I am not sure the underlying reason though.

[@bethcox7889]

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

[@Squash101]

45

[@saljimenez7071]

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?

[@saljimenez7071]

im am speaking about g(x)=x4-9x3+21x2+21x-130

[@shravans7184]

@@saljimenez7071 Yes we have either 3 or 1 positive X intercept while only 1 Negative X intercept.... after getting the solution that gets validated x=5 and x=-2 are the + and - x intercepts respectively..... rest being irreducible quadratics never touches the X intercept.... Appreciate you brother ... try to incorporate previous points so that we will never miss those ideas ...

[@gradhd4359]

june 14 2022

[@scopeless22]

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.

[@rosepierce9382]

How do you do that and still understand everything he says? I lose track very quickly.

[@scopeless22]

@@rosepierce9382 I've always been a fast talker, so I guess I'm just used to listening to fast talkers. He talks very slow to me in normal speed, so if I really need to pay attention I still have him at 1.5 speed.

[@rosepierce9382]

@@scopeless22 I tried doing that, because it'd save me a LOT of time, but ended up going back to normal speed. Oh, well. I am also taking notes, so yeah. Anyways, thanks for replying and hope you have the most wonderful day!

[@MerchantGuy-i1n]

​@@scopeless22 THE EXACT SAME THING HAPPENED TO ME TOO 😂

[@HritikJain]

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

[@josemaria_landa]

Thats a pretty vague question.