SOLUTION: Show that (x-1) (x+1) is a factor of f(x)=3x^50-3

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Question 1177057: Show that (x-1) (x+1) is a factor of f(x)=3x^50-3
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!



zeros are
....since factor , we have


.....no matter what root is it, solutions are
or
using root product theorem, we have

so, it is a factor of

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

3x^50 - 3 = 3*(x^50-1) = 3*((x^2)^25-1) = 3*(x^2-1)*(1 + x^2 + x^4 + x^6 + . . . + x^48).


Here I used the formula for the sum of an geometric progression


    1 + z + z^2 + z^3 + . . . + z^(n-1) = 


with z = x^2.

Solved.



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