[กขฃคฅฆง]

20. $g(x)=\dfrac{x^6-1}{x-1} $

จาก $x^6-1\mid x^{6k}-1 \qquad \forall k \in \mathbb{N} $

$\therefore x^6-1\mid (x^{60}-1)+(x^{48}-1)+(x^{36}-1)+(x^{24}-1)+(x^{12}-1)+(1-1) = g(x^{12})-6$

$\therefore \frac{x^6-1}{x-1} \mid g(x^{12})-6$

$g(x^{12}) = g(x)q(x) + 6$

เศษคือ 6