Find the remainder ax3+ax2+ax+c Is divided by ax+c?

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Find the remainder ax3+ax2+ax+c Is divided by ax+c?

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Answer 1 · 2018-02-21T14:40:20

$\frac{a x^{3} + a x^{2} + a x + c}{a x + c} = (x^{2} + x + 1) R (- c x^{2} - c x + c)$ $(ax^3+ax^2+ax+c)/(ax+c)=(x^2+x+1 )R(-cx^2-cx+c)$

Explanation:

....................... $x^{2} + x + 1$ $x^2+x+1$
$a x + c \sqrt{a x^{3} + a x^{2} + a x + c}$ $ax+csqrt(ax^3+ax^2+ax+c)$
................- $a x^{3} + c x^{2}$ $ax^3+cx^2$
................---------------..............
.................. $a x^{2} - c x^{2} + a x$ $ax^2-cx^2+ax$
................- $(a x^{2} + c x)$ $(ax^2+cx)$
................---------------..............
................................ $- c x^{2} - c x + c$ $-cx^2-cx+c$

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Find the remainder ax3+ax2+ax+c Is divided by ax+c?

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