In algebra, synthetic division is a method of performing polynomial long division, with less writing and fewer calculations. It is mostly taught for division by binomials of the form
but the method generalizes to division by any monic polynomial.
The most useful aspects of synthetic division are that it allows one to calculate without writing variables and uses fewer calculations. As well, it takes significantly less space than long division. Most importantly, the subtractions in long division are converted to additions by switching the signs at the very beginning, preventing sign errors.
Synthetic division for linear denominators is also called division through Ruffini's rule.
Read more about Synthetic Division: Regular Synthetic Division
Famous quotes containing the words synthetic and/or division:
“In every philosophical school, three thinkers succeed one another in the following way: the first produces out of himself the sap and seed, the second draws it out into threads and spins a synthetic web, and the third waits in this web for the sacrificial victims that are caught in it—and tries to live off philosophy.”
—Friedrich Nietzsche (1844–1900)
“For in the division of the nations of the whole earth he set a ruler over every people; but Israel is the Lord’s portion: whom, being his firstborn, he nourisheth with discipline, and giving him the light of his love doth not forsake him. Therefore all their works are as the sun before him, and his eyes are continually upon their ways.”
—Apocrypha. Ecclesiasticus 17:17-9.