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

(x^{29} - x^{25} + x^{13} - 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 x^{29} - x^{25} + x^{13} - 1 zero, so (x - 1) is its factor.

And, x= -1 does not make it zero.

So, (x + 1) is not its factor.