One satisfying factoring problem x^5+x^4+1

you're currently carrying my math grade

i feel so satisfied

I did it a slightly different way. Instead of adding and subtracting x^3 + x^2 + x, I only added and subtracted x^3. So x^5 + x^4 + 1 = x^5 + x^4 + x^3 + 1 - x^3 = (x^5 + x^4 + x^3) - (x^3 - 1) = x^3(x^2 + x + 1) - (x - 1)(x^2 + x + 1) = (x^3 - x + 1)(x^2 + x + 1).

indeed satisfying

I love complex world

The marker switch is so smooth

Try x^6+x^5+x^2

you are the GOAT!!

Great, thanks.

Really really really cunning and nice!!!!!

Factor theorem my beloved

Symbolab says cannot factor further

ω

ahh yes, another wild sighting of adding zero to an equation

Just factor it in Z mod 3 😂

Hey I have been watching you for a long time now , I'm just curious about where did you study or pursue your mathematical education?

cool

What is the cubic equation??

Is it naive to think that x^a+x^b+1 where a,b are non-negative integers, there exists a factorization that is not just 1 * (x^a+x^b+1)

Notice that 5, 4 and 0 (from 1=x⁰) form a complete residue class mod 3, so it's divisible by x²+x+1