Problem of the Week

Updated at Dec 29, 2025 4:22 PM

How would you solve the equation \(z({z}^{2}-3)=2\)?

Below is the solution.



\[z({z}^{2}-3)=2\]

1
Expand.
\[{z}^{3}-3z=2\]

2
Move all terms to one side.
\[{z}^{3}-3z-2=0\]

3
Factor \({z}^{3}-3z-2\) using Polynomial Division.
\[({z}^{2}-z-2)(z+1)=0\]

4
Factor \({z}^{2}-z-2\).
\[(z-2)(z+1)(z+1)=0\]

5
Solve for \(z\).
\[z=2,-1\]

Done
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