How do you factor completely: #10x^5 + 4x^4 + 8x^3#?
First we take out the obvious common factor of
That's pretty good. If we can factor the quadratic equation we can make more progress. To check if we can, we can check if the discriminant
Depending on what grade we're in, we either stop here or factor using complex numbers. I'll continue.
Pro tip: The Shakespeare Quadratic Formula (
By the Shakespeare Quadratic Formula the quadratic has zeros
so we can factor
and the entire expression