i need help with factoring

[kkiceman14]

I need to factor this:

x^8 - 1

i got this (x^4 - 1)(x^4 + 1)

i need to go farther how do i do that?

 

[tkhunny]

Keep going. Can you do the same thing with that x⁴ - 1?

 

[kkiceman14]

i think

(x^2 + 1)(x^2 - 1) (x^2 - 1)(x^2 -1)

 

[kkiceman14]

i think

(x^2 + 1)(x^2 - 1) (x^2 - 1)(x^2 -1)

do i keep going after that

 

[Denis]

i think
(x^2 + 1)(x^2 - 1) (x^2 - 1)(x^2 -1)
do i keep going after that

NO; (x^2 - 1)(x^2 - 1) = x^4 - 2x^2 + 1

(x^2 + 1)(x^2 - 1) (x^4 + 1) is all she wrote!

BUT BUT: how bouts (x^2 - 1) :?:

 

[stapel]

Note for test: Whenever you apply the "difference of squares" formula in a context like this (where at least one of the terms wasn't a square, but was a square to some power), always check to see if you can factor further.

Problems where you don't notice that you can "go further" with the factoring are a common trick question. Be prepared. :wink:

Eliz.