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 :)

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.

If you factor 1 - x^{5} in this way: 1 - x^{5} = (1 + x)(1 + x^{2} + x^{3} + x^{4}),

you can get your answer.