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Calculate the value  Use the synthetic division to find the quotient and the remainder $\left( 2x ^{ 3 } -x-1 \right) \div \left( x+1 \right)$
$\dfrac { 2 x ^ { 3 } - x - 1 } { x + 1 }$
Arrange the rational expression
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { 2 x ^ { 3 } - x - 1 } { x + 1 } }$
 Quotient $: 2 x ^ { 2 } - 2 x + 1 \\$ Remainder $: - 2$
Use the synthetic division to find the quotient and the remainder
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
 Divide $2 x ^ { 3 } - x - 1$ by $x + 1$ using the synthetic division 
 Quotient $: 2 x ^ { 2 } - 2 x + 1 \\$ Remainder $: - 2$
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