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:
“That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prized—all these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.”
—Fred Rogers (20th century)
“It is never the thing but the version of the thing:
The fragrance of the woman not her self,
Her self in her manner not the solid block,
The day in its color not perpending time,
Time in its weather, our most sovereign lord,
The weather in words and words in sounds of sound.”
—Wallace Stevens (1879–1955)