SOLUTION: I have been having trouble on this problem for awhile now and I was wondering if anyone could help me? Please and Thank You!! I would deeply appreciate it! Factor completely. c

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: I have been having trouble on this problem for awhile now and I was wondering if anyone could help me? Please and Thank You!! I would deeply appreciate it! Factor completely. c      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 137778This question is from textbook Algebra Structure and Method
: I have been having trouble on this problem for awhile now and I was wondering if anyone could help me? Please and Thank You!! I would deeply appreciate it!
Factor completely. check for a greatest common factor first.
X^8-1 This question is from textbook Algebra Structure and Method

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Problems of the form
z%5E2-b%5E2 factor in this fashion
z%5E2-b%5E2=%28z-b%29%28z%2Bb%29
We can make a substitution to get it into this form.
Let
z=x%5E4
b=1
Therefore
z%5E2-b%5E2=x%5E8-1=%28x%5E4-1%29%28x%5E4%2B1%29
Similarly
x%5E4-1=%28x%5E2-1%29%28x%5E2%2B1%29
and
x%5E2-1=%28x-1%29%28x%2B1%29
Substituting all of those in, you get
x%5E8-1=%28x-1%29%28x%2B1%29%28x%5E2%2B1%29%28x%5E4%2B1%29
The roots of x%5E2%2B1 are (i, -i).
x%5E8-1=%28x-1%29%28x%2B1%29%28x%2Bi%29%28x-i%29%28x%5E4%2B1%29
Finally if we do a substitution of u=x%5E2 we get,


When we put that all together we get,

You can check on the square root of i and -i.
The four roots are of the form
x=0+%2B-+%281%2Fsqrt%282%29%29%281+%2B-+i%29