Question 403541
There's a nice theorem (fairly difficult to prove though) called the fundamental theorem of algebra that says that any n-degree polynomial has n complex roots, including multiple roots. Therefore we expect five roots.


Factoring the expression, this becomes


{{{k^3(k^2 + 4k - 32) = 0}}} --> {{{k^3 = 0}}} or {{{k^2 + 4k - 32 = 0}}}


The first equation has a triple root of 0. The second equation can be factored as {{{(x + 8)(x - 4) = 0}}} --> x = -8, x = 4.