Solving Polynomial Equations (1 of 2: Using the factor theorem)

[@vinodmahes8243]

You make maths interesting 💯❤

[@arnav5112]

THANK YOU SO MUCH. Your way of teaching is just amazing! You make it so easy to understand and make it interesting.

[@gedlangosz1127]

Just be a bit careful using this trick. By the "factor theorem", any rational roots will be one of: ±1, ±3, ±1/2, ±3/2. You are NOT guaranteed a root of 3 or -3. You are NOT guaranteed any rational roots either. In fact you may not have any real roots at all. If you suspect rational roots then look for the easier roots of 1 and -1 first. It happens that both of these work. The whole thing then easily factorieses to (x + 1)(x - 1)(x - 3)(2x + 1). No need for calculators. IMHO they should only be allowed in a maths class when doing trigonometry or numerical analysis.

[@aashsyed1277]

BY THE RATIONAL ROOT THEOREM

[@astecheee1519]

Teacher here - I mistakenly gave a student exactly this kind of trap question just yesterday. That's a cold shock of an introduction to complex numbers! Personally, I find this to be a very weird topic to teach in high school. Understanding the mechanisms of factorisation isn't as important as understanding how a derivative works, or a probability density function. I bet that within 50 years factorisation like this will be relegated to the calculator as well.

[@gauravbatra9987]

Oh thank you, you solved my confusion.

[@gauravbatra9987]

@@aashsyed1277 Thank you for pointing out the exact name.

[@aashsyed1277]

@@gauravbatra9987 bro u replied to me 2 years later I don't even watch this channel bow

[@JanickGers0]

Just one question, why aren't you using Ruffini's Rule to do polynomial division at this point? They're all gonna be linear factors, it's easier and faster than doing long division and there are fewer chances for mistakes.

[@shandyverdyo7688]

Is that Horner?

[@gedlangosz1127]

I'd not come across Ruffini's rule before. Neat. Using this, you do not need calculators to check for factors of (x + 3) and (x - 3).

[@JanickGers0]

@@gedlangosz1127 Exactly. You can practically skip the remainder theorem, specially for longer polynomials. It's very useful!

[@jackthechristian2820]

@@JanickGers0 But can you divide a bigger polynomial with x^2+5 for example.

[@aashsyed1277]

@@JanickGers0 what is the ruffini rule? give me a link

[@Spyrovins]

What a legend. Saved my ass literally

[@emilywong4601]

When will part 2 be uploaded?

[@alwysrite]

nice trick for last term

[@SgtAhmad]

P(-3)=240

[@christophersedlak1147]

thanks

[@aaaight]

Are the students allowed to use calculators in exams?

[@jackthechristian2820]

Yes. High school maths in Australia ALWAYS allow calculators.

[@sukesheducation]

@@jackthechristian2820 thats pretty damm cool

[@aayan-m5005]

I love you eddie woo

[@kwaleyelainonge7482]

I am highly lost on how to solve a polynomial equation without factor that zero it x³+9x²-10x-34=0 without using graphing calculator

[@thatomofolo452]

[@SumeetKumarHC]

Maths make him interesting

[@aashsyed1277]

he makes maTH INTERESTING

[@Aless6ClubTM]

Guys its 00:00 what’s wrong with u

[@madjidaoumeur7927]

I just want to ask, do you biloeve that exists?

[@naifdayil8165]

I had no idea why I'm here but p(-3)=240

[@HimeshIITK]

Indian scools dont allow calculators in class

[@dumpling01]

What no, I use it

[@jackthechristian2820]

Well, good luck doing quadratic formula with really long numbers without a calculator.

[@jackthechristian2820]

no calculator just means easier tests. you can only go so far without calculators.

[@carultch]

@@jackthechristian2820 It also means that they have to do more work setting up examples, to deliberately rig the problems to come out nicely.

[@foxcelius95]

XD

[@mizou9669]

first

[@tanish7623]

This is ez claps and i'm 13

[@kevinguacamole5300]

me too :) but this is not ez claps