Algebra and Applications Test 2

Question : 22 of 40

Marks: +1, -0

Which one of the following is divisible by

(1 + q + q^5 )

and

(1 + q^4 + q^5 )

individually?

$(q^2 + q + 1)$ $(q^3 + q^2 + 1)$ $(q^3 + q + 1)$
$(q^4 - q + 1) (q^3 + q^2 + 1) (q^3 + q - 1)$
$(q^4 + q + 1) (q^3 - q^2 + 1) (q^3 + q + 1)$
$(q^2 + q + 1) (q^3 - q^2 + 1) (q^3 - q + 1)$
None of these

Solution:

(1 + q + q^5 ) (1 + q^4 + q^5 )

=1+q+q^4+3q^5+q^9+q^10

Also,

(q^2 + q + 1) (q^3 - q^2 + 1) (q^3 - q + 1)

=1+q+q^4+3q^5+q^9+q^10

∴ (q^2 + q + 1) (q^3 - q^2 + 1) (q^3 - q + 1)

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