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

If (x + 1/x) = 2, then (x31/x3) is equal to :

Option:
A. 64
B. 14
C. 8
D. 2
Answer: D . 2

Justification:

x + 1/x = 2

→ ( x + 1/x)3 = 23

→ x3 + 1/x3 +3(x + 1/x) = 8

→ x3 + 1/x3 + 3 x 2 = 8

→ x3 + 1/x3 = 2.

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