Question 13

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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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