We can rewrite the cubic equation x3−100x=0 into one linear equation and one quadratic equation by factoring out x.x(x2−100)=0.
By using the Zero Product Property, we can now rewrite this equation into the two simpler equations
From the first equation we learn that x=0 is a solution. Let's go on and solve the second equation.
We will now use the Zero Product Property and rewrite the equation into
As before, we find that one solution is x=0. By solving the second equation we will find an additional two solutions.
We have found the three solutions of the equation and they are
This time, we have a quartic equation, x4−8x=0. Just as before, it is possible to factor out an x. Then, we get
and the Zero Product Property gives us the two equations
From the first we learn, as previously, that x=0 is a solution. The second equation is a cubic equation. Let's solve it.