Editing Synthetic division (section)

===Evaluating polynomials by the remainder theorem===

The above form of synthetic division is useful in the context of the [[polynomial remainder theorem]] for evaluating [[univariate]] polynomials. To summarize, the value of <math>p(x)</math> at <math>a</math> is equal to the [[remainder]] of the division of <math>p(x)</math> by <math>x-a.</math>

The advantage of calculating the value this way is that it requires just over half as many multiplication steps as naive evaluation. An alternative evaluation strategy is [[Horner's method]].