Mathematical Induction: Polynomial Divisibility Proof

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I enjoy all of your videos. Please continue posting these! Just awesome.

misteralias

This is a nice use of induction for a more complicated situation!

(Even though in reality induction is unnecessary since you can prove this using the factor theorem in about 1 line of working.)

mxlexrd

Your videos' are really great. I enjoy them and hope to become a teacher like you in future.
Love from India.

sujoyghosh

Interesting problem! But my "increasing gap" trick absolutely destroys it as usual. ;)
(x^(n+1)-1)-(x^n-1)
=x^(n+1)-x^n
=x×x^n-x^n
=(x-1)×x^n
I didn't even need to think at all about this, the usual first steps were already enough. Since you announced the 10 minutes at the start, I measured my time: This took me 3min10sec, including writing down the initial claim (with the ≥ character, for which I needed to use an on-screen keyboard) and a check for n=0, n=1 and n=2.
Also, the n≥2 restriction is not necessary:
x⁰-1=0
x¹-1=x-1

do you still teach ipt because i'm still using your ipt lessons to help myself studies and understand some things in ipt

haz

I was mentally subtracting and adding x^k and got thrown when that wasn't how you did it. Different process, same result.

redpenofdoom

Amazing as usual keep up the good work 😊😊

davidmaxen

Can't u just prove it by saying that

A polynomial which is divisibile by x-k just means that k has to be a root of the polynomial. 1^n -1 is 0 for every n. Done

davidepierrat

after 4 days of watching all of your mathematical induction videos and practicing as much as I can, mathematical induction still sucks

iledesma

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