Synthetic Division (Ruffini's Rule)

​
polynomial degree
4
new example
p(x) =
4
x
+4
3
x
-29
2
x
+24x
4
x
+4
3
x
-29
2
x
+24x
1
4
-29
24
0
1
1
5
-24
0
1
5
-24
0
0
3
x
+5
2
x
-24x
1
5
-24
0
3
3
24
0
1
8
0
0
2
x
+8x
1
8
0
-8
-8
0
1
0
0
x
1
0
0
0
1
0
p(x) = (x-3)(x-1)x(x+8)
Ruffini's rule is a method that allows the rapid division of a polynomial by a binomial of the form
x-r
, where
r
is one of the roots of the polynomial.

Details

Synthetic division is a shortcut method for dividing a polynomial by a linear factor of the form
x-r
, where r is a root of the polynomial. It can be used instead of the standard long division algorithm. This method reduces the polynomial and the linear factor into a set of numeric values. After these values are processed, the resulting set of numeric outputs is used to construct the polynomial quotient and the polynomial remainder.
​

External Links

Synthetic Division (Wolfram MathWorld)

Permanent Citation

Eugenio Bravo
​
​"Synthetic Division (Ruffini's Rule)"​
​http://demonstrations.wolfram.com/SyntheticDivisionRuffinisRule/​
​Wolfram Demonstrations Project​
​Published: March 19, 2008