**Division of a
Polynomial by a Binomial / **polynomial

**Ruffini's Rule: **The rule allows for the quick
division of a polynomial **f(x**) by a binomial of the form **(x-r)**
where where x is a variable and r is an integer. A polynomial of degree zero is
called a constant, degree 1 a linear polynomial, degree 2 as a quadratic
polynomial, degree 3 as a cubic polynomial, degree 4 as quartic polynomial etc.
Zero polynomial is different from a polynomial of degree zero in the sense that
its degree is either -1 or -infinity. Polynomial of one variable is called a
univariate, of two variables a bivariate or more than 3 multivariate. A
polynomial of more than 1 variable is called homogenous of degree n if all the
terms are of degree n. A **monic polynomial** is a
polynomial
in which the leading coefficient *c*_{n} is equal to 1.

The division of a polynomial by a polynomial is through synthetic division.

Ruffini's rule is the **special case of synthetic division
**where the **divisor is a linear factor.** The scheme was devised by **Paolo Ruffini,**
an Italian mathematician of late Eighteenth and early Nineteenth century. Ruffini
was born in Valentano, a small town in Italy famous for its fortress and
churches in the year 1765.At the age of 23, he earned University degree in
philosophy, mathematics and medicine & surgery. He worked both as a doctor and a
Professor of mathematics. He made significant contribution to the group theory,
probability and computational mathematics. Ruffini died in 1822.

f (x) = **
x ^{3}** +

f_{1}(x) = **x** -

f_{2}(x) =
**
x ^{2}** +

**f (x)/f _{1}(x)** =

and
* remainder*)

**f (x)/f _{2}(x)** =

and
**x ^{1}** +