Solve the polynomial inequality and graph the solt $$ x^{3}+3 x^{2}-9 x-270 $$

Question

Solve the polynomial inequality and graph the solt $$ x^{3}+3 x^{2}-9 x-27>0 $$

UpStudy AI · Accepted Answer

The solution is $$x>3$$. Solve the equation $$ x^{3}+3 x^{2}-9 x-27>0 $$. Solve the inequality by following steps: - step0: Solve the inequality by testing the values in the interval: $$x^{3}+3x^{2}-9x-27>0$$ - step1: Rewrite the expression: $$x^{3}+3x^{2}-9x-27=0$$ - step2: Factor the expression: $$\left(x-3 ight)\left(x+3 ight)^{2}=0$$ - step3: Separate into possible cases: $$\begin{align}&x-3=0\&\left(x+3 ight)^{2}=0\end{align}$$ - step4: Solve the equation: $$\begin{align}&x=3\&x=-3\end{align}$$ - step5: Determine the test intervals: $$\begin{align}&x<-3\&-33\end{align}$$ - step6: Choose a value: $$\begin{align}&x_{1}=-4\&x_{2}=0\&x_{3}=4\end{align}$$ - step7: Test the chosen value: $$\begin{align}&x<-3 extrm{ } extrm{is not a solution}\&-33 extrm{ } extrm{is the solution}\end{align}$$ - step8: The final solution is $$x>3:$$ $$x>3$$ The solution to the polynomial inequality $$x^{3}+3x^{2}-9x-27>0$$ is $$x>3$$. Unfortunately, I am unable to plot the graph for you at the moment.

Solve the polynomial inequality and graph the solt \[ x^{3}+3 x^{2}-9 x-27>0 \]

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Solve the polynomial inequality and graph the solt \[ x^{3}+3 x^{2}-9 x-27>0 \]

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