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avatar+993 

Given \(x\) so that \(x + x^2 + x^3 + x^4 = 5\), what is the value of \({1 - x^5\over{1-x}}\)?

 

Not sure where to start or what to subsitute for this problem... help please thanks :)

 Feb 17, 2022
 #1
avatar+993 
+3

The answer was 6...

 

Using synthetic division it says that 1-x^5 / 1-x = 1 + x + x^2 + x^3 + x^4, I don't get this "synthetic division" could someone explain to me how it really works. 

 Feb 17, 2022
 #2
avatar+23209 
+2

If you factor  1 - x5  in this way:  1 - x5 =  (1 + x)(1 + x2 + x3 + x4),

you can get your answer.

 Feb 17, 2022

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