Category:Definitions/Synthetic Division

This category contains definitions related to Synthetic Division.
Related results can be found in Category:Synthetic Division.

Synthetic division is a technique for dividing a polynomial by a linear factor.

Let $\map P x$ be a polynomial of degree $n$.

Dividing $\map P x$ by $x - a$ we get:

$\map P x = \paren {x - a} \map Q x + r$

where $\map Q x$ is a polynomial of degree $n - 1$ and $r$ is a constant.

Applying Horner's rule to evaluate $\map P a$, the coefficient $a_n$ together with the intermediate quantities produced as each pair of brackets is removed are the coefficients of $\map q x$.

Hence the final result is $r = \map P a$.