Dividing polynomials is an important part of algebra. It's a way to get a "new" polynomial by combining two existing ones.
For instance, if you want the sum of two polynomials, you can just add their coefficients and divide by two (the degree). If you want to subtract one polynomial from another, you can do that too! You just keep dividing until you get as close as possible to 0.
The same goes for multiplying two polynomials: just multiply their coefficients and divide by the product of their degrees.
So what about division by a variable? Well, it's not quite as simple as taking the reciprocal. Instead, we use the FOIL method: First terms (a), Outer terms (b), Inner terms (c), and Last terms (d). Then we multiply them together! For example: if we wanted to find 4x divided by 2x+4y-5z then we'd write: (4x)(2x+4y-5z).
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