Jambmaths question:
Find the remainder when ${{x}^{3}}-2{{x}^{2}}+3x-3$is divided by ${{x}^{2}}+1$
Option A:
$2x+1$
Option B:
$x-3$
Option C:
$x+3$
Option D:
$2x+1$
Jamb Maths Solution:
$\begin{align} & {{x}^{2}}+1\overset{x-2\text{ }}{\overline{\left){\begin{align} & {{x}^{3}}-2{{x}^{2}}+3x-3 \\ & \underline{{{x}^{3}}\text{ + }x} \\ & \text{ }-2{{x}^{2}}+2x-3 \\ & \text{ }\underline{\text{ }-2{{x}^{2}}\text{ }-2\text{ }} \\ & \text{ }2x+1 \\ & \text{ } \\\end{align}}\right.}} \\ & \therefore \frac{{{x}^{3}}-2{{x}^{2}}+3x-3}{{{x}^{2}}+1}=x-2+\frac{2x+1}{{{x}^{2}}+1} \\ & \text{The remainder is }2x+1 \\\end{align}$
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