Explanation:
In mathematics, a polynomial (from Greek poly, "many" and medieval
Latin binomium, "binomial") is an expression of finite length constructed from variables (also known as indeterminates)
and constants, using only the
operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x^{2} − 4x + 7 is a polynomial, butx^{2} − 4/x + 7x^{3/2} is not, because its second term involves division by the
variable x (4/x) and because its third
term contains an exponent that is not a whole number (3/2).
http://en.wikipedia.org/wiki/Polynomial
Polynomial
remainder theorem
In algebra, the polynomial remainder
theorem or little theorem is an application of polynomial long
division. It states that the remainder of a polynomial divided by a linear divisor is equal to (Our solved example in mathguru.com uses
this concept).
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:
Applications
The polynomial remainder theorem may be used to evaluate by calculating the remainder, r.
Although polynomial long division is more difficult than evaluating the function itself, synthetic division is computationally easier. Thus, the
function may be more "cheaply" evaluated using synthetic division and
the polynomial remainder theorem.
The factor theorem is another application of the
remainder theorem: if the remainder is zero, then the linear divisor is a
factor. Repeated application of the factor theorem may be used to factorize the
polynomial.
http://en.wikipedia.org/wiki/Polynomial_remainder_theorem
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