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Calculate the value
Answer
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Use the synthetic division to find the quotient and the remainder
Answer
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$\left( x ^{ 2 } +x+2 \right) ^{ 3 } \div \left( x ^{ 2 } +1 \right)$
$\dfrac { x ^ { 6 } + 3 x ^ { 5 } + 9 x ^ { 4 } + 13 x ^ { 3 } + 18 x ^ { 2 } + 12 x + 8 } { x ^ { 2 } + 1 }$
Arrange the rational expression
$\left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \div } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { x ^ { 6 } + 3 x ^ { 5 } + 9 x ^ { 4 } + 13 x ^ { 3 } + 18 x ^ { 2 } + 12 x + 8 } { x ^ { 2 } + 1 } }$
$ $ Quotient $ : x ^ { 4 } + 3 x ^ { 3 } + 8 x ^ { 2 } + 10 x + 10 \\ $ Remainder $ : 2 x - 2$
Use the synthetic division to find the quotient and the remainder
$\left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 3 } } \div \left ( x ^ { 2 } + 1 \right )$
$ $ Calculate power $ $
$\left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 13 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 18 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \right ) \div \left ( x ^ { 2 } + 1 \right )$
$\left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 13 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 18 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$ $ Divide $ x ^ { 6 } + 3 x ^ { 5 } + 9 x ^ { 4 } + 13 x ^ { 3 } + 18 x ^ { 2 } + 12 x + 8 $ by $ x ^ { 2 } + 1 $ using the synthetic division $ $
$ $ Quotient $ : x ^ { 4 } + 3 x ^ { 3 } + 8 x ^ { 2 } + 10 x + 10 \\ $ Remainder $ : 2 x - 2$
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