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

If x + y + z = 9  &  xy + yz + zx = 23,
then the value of (x3 + y3 + z3 - 3xyz) is :

Option:
A. 108
B. 207
C. 669
D. 729
Answer: A . 108

Justification:

-> (x3 + y3 + z3 - 3xyz)
= (x + y + z) (x2 + y2 + z2 - xy - yz - zx)
= (x + y + z) [(x + y + z)- 3(xy + yz + zx)]
= 9 x (81 - 3 x 23)
= (9 x 12)
= 108

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