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# clever algebraic manipulations help...

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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
+516
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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
+23183
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If you factor  1 - x5  in this way:  1 - x5 =  (1 + x)(1 + x2 + x3 + x4),