The document discusses the remainder theorem in polynomials, which states that the remainder of dividing a polynomial P(x) by a binomial x - a is equal to P(a). It provides an example of using synthetic division and the remainder theorem to find the remainder, and notes that if the remainder is 0, then the binomial is a factor of the original polynomial. The document also gives an example problem of determining the value of k when dividing a polynomial by a binomial that gives a remainder of 1.

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Remainder Theorem

2. January 13, 2010
Remainder Theorem
If P(x) is a polynomial and you divide it by
a binomial x - a, then the remainder will be
P(a)
Let's see how it works!!
Find the remainder both by using synthetic division
and by using the remainder theorem

3. January 13, 2010
Find the remainder both by using synthetic division
and by using the remainder theorem

4. January 13, 2010
Find the remainder both by using synthetic division
and by using the remainder theorem

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If we find the remainder to be 0,
what does it tell us about the
relationship between the binomial
divisor and the polynomial?????

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If you find the remainder to be 0 when
dividing a polynomial by a binomial,
then the binomial is a factor of the
polynomial!!!!

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Determine each value of k.
(a) When x 3 + kx2 + 2x - 3 is divided by x + 2, the remainder is 1.

8. January 13, 2010