Question

Perform the Indicated operation

(x+1)^3 in Z3[x]

Answer 1

\[ (x+1)^{3} in Z_{3}[x]\]

Answer 2

\[\huge (x+1)^3 \ \ \ \ in \ \mathbb{Z}_3[x]\]
LOL any idea how to do this? :)

Answer 3

do i just use f(0) and f(1) to solve for them in Z3? I'm not sure really thats why I'm asking and my book doesn't even address it.

Answer 4

hint \(3\equiv 0\)

Answer 5

Freshman's dream :D
Anyway, evaluate this
(x+1)^3 normally first, and tell me what you get.

Answer 6

lol

Answer 7

Cube of a binomial?

Answer 8

1+3 x+3 x^2+x^3

Answer 9

That's right :)
\[\huge x^3 + 3x^2+3x+1\]but... we take everything in mod 3...
In particular, in
\[\large \mathbb{Z}_3\]
3=0, right?

Answer 10

yes

Answer 11

so is it X^3 + 1?

Answer 12

You got it :)
And now, for any prime number p

Answer 13

\[\huge (a+b)^p=a^p+b^p \ \ \ \ \ in \ \mathbb{Z}_p\]

Answer 14

i always suspected my math teachers were lying, and \((a+b)^3=a^3+b^3\)

Answer 15

Oh abstract algebra... so deceptive :D
That was fun... but I'm getting drowsy :/
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Terence out

Answer 16

Thank you