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Formula
Solve the equation
Answer
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Graph
$y = \left ( x + 2 \right ) \left ( x ^ { 2 } - 3 x + 4 \right )$
$y = 0$
$x$Intercept
$\left ( - 2 , 0 \right )$
$y$Intercept
$\left ( 0 , 8 \right )$
Derivative
$3 x ^ { 2 } - 2 x - 2$
Seconde derivative
$6 x - 2$
Local Minimum
$\left ( \dfrac { 1 } { 3 } + \dfrac { \sqrt{ 7 } } { 3 } , - \dfrac { 2 \sqrt{ 7 } } { 3 } - \left ( \dfrac { 1 } { 3 } + \dfrac { \sqrt{ 7 } } { 3 } \right ) ^ { 2 } + \left ( \dfrac { 1 } { 3 } + \dfrac { \sqrt{ 7 } } { 3 } \right ) ^ { 3 } + \dfrac { 22 } { 3 } \right )$
Local Maximum
$\left ( \dfrac { 1 } { 3 } - \dfrac { \sqrt{ 7 } } { 3 } , - \left ( \dfrac { 1 } { 3 } - \dfrac { \sqrt{ 7 } } { 3 } \right ) ^ { 2 } + \left ( \dfrac { 1 } { 3 } - \dfrac { \sqrt{ 7 } } { 3 } \right ) ^ { 3 } + \dfrac { 2 \sqrt{ 7 } } { 3 } + \dfrac { 22 } { 3 } \right )$
Point of inflection
$\left ( \dfrac { 1 } { 3 } , \dfrac { 196 } { 27 } \right )$
$\left( x+2 \right) \left( x ^{ 2 } -3x+4 \right) = 0$
$\begin{array} {l} x = - 2 \\ x = \dfrac { 3 + \sqrt{ 7 } i } { 2 } \\ x = \dfrac { 3 - \sqrt{ 7 } i } { 2 } \end{array}$
Solve the equation
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) = \color{#FF6800}{ 0 }$
$ $ At least one factor should be 0 $ $
$\begin{array} {l} \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } = \color{#FF6800}{ 0 } \\ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } = \color{#FF6800}{ 0 } \end{array}$
$\begin{array} {l} \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } = \color{#FF6800}{ 0 } \\ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } = \color{#FF6800}{ 0 } \end{array}$
$ $ Solve each equation $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 + \sqrt{ 7 } i } { 2 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 - \sqrt{ 7 } i } { 2 } } \end{array}$
$x ^ { 3 } - x ^ { 2 } - 2 x + 8 = 0$
Solve the fractional equation
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) = \color{#FF6800}{ 0 }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } = \color{#FF6800}{ 0 }$
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