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Basic operations, simple factors, factor Theorem, Remainder Theorem, Division of polynomials.

(x29 - x25 + x13 - 1) is divisible by:

Option:
A. both (x - 1) & (x + 1)
B. (x - 1) but not by (x + 1)
C. (x + 1) but not by (x - 1)
D. neither (x - 1) nor (x + 1)
Answer: B . (x - 1) but not by (x + 1)

Justification:

Since x = 1 makes x29 - x25 + x13 - 1 zero, so (x - 1) is its factor.
And, x= -1 does not make it zero.
So, (x + 1) is not its factor. 

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