Proof
The polynomial remainder theorem follows from the definition of polynomial long division; denoting the divisor, quotient and remainder by, respectively, and, polynomial long division gives a solution of the equation
where the degree of is less than that of .
If we take as the divisor, giving the degree of as 0, i.e. :
Setting we obtain:
Read more about this topic: Polynomial Remainder Theorem
Famous quotes containing the word proof:
“A short letter to a distant friend is, in my opinion, an insult like that of a slight bow or cursory salutation—a proof of unwillingness to do much, even where there is a necessity of doing something.”
—Samuel Johnson (1709–1784)
“From whichever angle one looks at it, the application of racial theories remains a striking proof of the lowered demands of public opinion upon the purity of critical judgment.”
—Johan Huizinga (1872–1945)
“The proof of a poet is that his country absorbs him as affectionately as he has absorbed it.”
—Walt Whitman (1819–1892)