A polynomial expression is one that contains several algebraic terms, such as
3x4 - 5x3 + 2x2 + 3x - 2
It is common to write a polynomial expression with terms in decreasing order (x4, x3, x2 etc).
When we divide a polynomial expression by a given term, we divide each term in turn.
Divide by 2x3:
8x14 - 6x8 + 2x4 - 4x3
We divide each term in turn, remembering to subtract indices and divide coefficients.
This simplifies to
4x11 - 3x5 + x - 2