Synthetic division can only be used if you're dividing by a LINEAR factor in the form x - a. For example, it works if you are dividing by x - 3 or by x + 4. If you need to divide by a polynomial with a higher degree or one that doesn't have a 1 as the leading coefficient, you'll have to do plain old long division.
In algebra, the composite division is a manual way of performing Euclidean division of polynomials that requires less writing and less computation than long division.
Primarily described for division by a linear singular polynomial (known as Ruffini's rule), but the method can be generalized to division by any polynomial.
The advantage of compound division is that it can be calculated without writing variables, requires very little calculation, and saves a lot of paper space over long divisions. The long division also converts subtraction to addition by exchanging the first sign. This avoids sign errors.
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