SOLUTION: Can someone show me how to factor: x^8 - 1 and x^4 + 2x^3 - 3x - 6 (Can this one even be factored?) Thanks in advance for your help. Not sure I ever learned this

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can someone show me how to factor: x^8 - 1 and x^4 + 2x^3 - 3x - 6 (Can this one even be factored?) Thanks in advance for your help. Not sure I ever learned this       Log On


   

Question 404577: Can someone show me how to factor:
x^8 - 1
and
x^4 + 2x^3 - 3x - 6 (Can this one even be factored?)
Thanks in advance for your help. Not sure I ever learned this stuff before but I sure look forward to it. I do have the basics down but really need the steps leading to the answer(s) Thanks again!
Mark
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E8+-+1..........8=2%2A2%2A2, so you can write %28%28x%5E4%29%5E2+%29%29%29 or
%28%28x%5E2%29%5E2%29%5E2+%29%29%29 ...same with 1

%28x%5E4%29%5E2+-%281%5E4%29%5E2.....use a rule for factoring a difference of squares

%28x%5E4+-1%5E4%29%28x%5E4%2B+1%5E4%29 ..............x%5E4=+%28x%5E2%29%5E2%29
and we have
%28%28%28x%5E2%29%5E2%29+-%28%281%5E2%29%5E2%29%29%28x%5E4%2B+1%29..factor this %28%28%28x%5E2%29%5E2%29+-%28%281%5E2%29%5E2%29%29

%28x%5E2+-1%29%28x%5E2+%2B1%29%28x%5E4%2B+1%29........factor+%7B%7B%7B%28x%5E2+-1%29

%28x+-1%29%28x+%2B1%29%28x%5E2+%2B1%29%28x%5E4%2B+1%29

and

x%5E4+%2B+2x%5E3+-+3x+-+6...group

%28x%5E4+%2B+2x%5E3%29+-+%283x+%2B+6%29

x%5E3%28x+%2B+2%29+-+3%28x+%2B+2%29.....common factor %28x+%2B+2%29

%28x+%2B+2%29%28x%5E3-+3%29