I was looking for the shipping forecast!
And you got the shitting forecast instead
Whoosh!
Totally over my head!
As you may remember, things like quadratic equations (where you have an x squared term) often have 2 solutions, and this extends to equations with higher powers in. You will also have covered that some of those equations apparently had no valid solutions (because the solutions required complex numbers, and you don’t cover those until later generally). What they’ve done here is work out the equation where one of the solutions is i8 (i being the square root of -1) and 8!, aka 8 factorial, so 8x7x6x5x4x3x2x1.
Then in first year uni (in my course), you learn that any polynomial has a root which the lecturer called a trade union theorem (one out, all out).
In second year you then learn that beyond 5th order (i.e. x⁵) there is no standard formula and hence the Rubik cube.
Out of interest, is it proved that there’s nothing beyond fifth order, or is it that we haven’t worked one out yet? I can imagine they get exponentially more complicated as the powers increase.