Formal Version
Let be a polynomial with complex coefficients, and be in an integral domain (e.g. ). Then if and only if can be written in the form where is also a polynomial. is determined uniquely.
This indicates that those for which are precisely the roots of . Repeated roots can be found by application of the theorem to the quotient, which may be found by polynomial long division.
Read more about this topic: Factor Theorem
Famous quotes containing the words formal and/or version:
“This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. It’s no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.”
—Leontine Young (20th century)
“If the only new thing we have to offer is an improved version of the past, then today can only be inferior to yesterday. Hypnotised by images of the past, we risk losing all capacity for creative change.”
—Robert Hewison (b. 1943)