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Formula
Calculate the value
Use the synthetic division to find the quotient and the remainder
$\left( 2x ^{ 4 } +25x ^{ 3 } +4x+10 \right) \div \left( 2x+1 \right)$
$\dfrac { 2 x ^ { 4 } + 25 x ^ { 3 } + 4 x + 10 } { 2 x + 1 }$
Arrange the rational expression
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { 2 x ^ { 4 } + 25 x ^ { 3 } + 4 x + 10 } { 2 x + 1 } }$
 Quotient $: x ^ { 3 } + 12 x ^ { 2 } - 6 x + 5 \\$ Remainder $: 5$
Use the synthetic division to find the quotient and the remainder
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
 Divide $2 x ^ { 4 } + 25 x ^ { 3 } + 4 x + 10$ by $2 x + 1$ using the synthetic division 
 Quotient $: x ^ { 3 } + 12 x ^ { 2 } - 6 x + 5 \\$ Remainder $: 5$
Solution search results