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Formula
Calculate the value
Use the synthetic division to find the quotient and the remainder
$\left( x ^{ 3 } -3x ^{ 2 } +5x+4 \right) \div \left( x-2 \right)$
$\dfrac { x ^ { 3 } - 3 x ^ { 2 } + 5 x + 4 } { x - 2 }$
Arrange the rational expression
$\left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { x ^ { 3 } - 3 x ^ { 2 } + 5 x + 4 } { x - 2 } }$
 Quotient $: x ^ { 2 } - x + 3 \\$ Remainder $: 10$
Use the synthetic division to find the quotient and the remainder
$\left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
 Divide $x ^ { 3 } - 3 x ^ { 2 } + 5 x + 4$ by $x - 2$ using the synthetic division 
 Quotient $: x ^ { 2 } - x + 3 \\$ Remainder $: 10$
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