What is the Rest Theorem? »Its Definition and Meaning [2019]

Theorem of rest is a practical method that is used to divide a polynomial P (x) by another whose shape is xa; in which only the rest value is obtained.

To apply this rule , the following steps are followed:

• Write the polynomial dividend without completing or ordering.
• Replace the dividend variable x with the opposite value of the term independent of the divisor.
• The operations are solved combined indicated.

The rest's theorem is a method by which we can obtain the residue of a division algebraic but in which it is not necessary to make any division.This allows us to find out the rest of the division of a polynomial p (x) among another of the form xa, for example.From this theorem it follows that a polynomial p (x) it is divisible by xa only if a is a root of the polynomial, only if and only if p (a)=0.If C (x) is the quotient and R (x) is the rest of the division of any polynomial p (x ) enter a binomial that would be (xa)

Then the value numeric of p (x), for x=a, is equal to the rest of its division by xa.Then we will say that:

P (a)=C (a) • (a-a) + R (a)=R (a)

In general, to obtain the rest of a division between Xa, it is more convenient to apply the rule of Ruffini than to replace the x.Therefore, the rest theorem is more suitable for problem solving .