synthetic division

[soandos]

so synthetic division can be used to divide polynomials by monomials. is there a to divide by
ax-b as opposed to x-b? ax^2-b? is there a general rule?
thanks.
or does one have to revert to polynomial long division.

[HallsofIvy]

"Synthetic division" is used specifically to divide a polynomial by "x- a" for some number a. That is a very important special case since it is so often important to find all roots of a polynomial equation and dividing by x-a when a is a root you have already found reduces the equation.

Of course, you can use regular algebraic division if the divisor is something like 3x- 2 or x^2+ 4x- 3.