Difference between revisions of "Remainder Theorem"
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=Theorem= | =Theorem= | ||
| − | The Remainder Theorem states that the remainder when the polynomial <math>P(x)</math> is divided by <math>x-a</math>(usually with synthetic division) is equal to the simplified value of <math>P(a)</math> | + | The Remainder Theorem states that the remainder when the polynomial <math>P(x)</math> is divided by <math>x-a</math> (usually with synthetic division) is equal to the simplified value of <math>P(a)</math> |
=Examples= | =Examples= | ||
Revision as of 18:08, 13 January 2016
Contents
Theorem
The Remainder Theorem states that the remainder when the polynomial 
is divided by 
(usually with synthetic division) is equal to the simplified value of 
Examples
Example 1
What is the remainder in 
?
Solution
Using synthetic or long division we obtain the quotient 
. In this case the remainder is 
. However, we could've figured that out by evaluating 
. Remember, we want the divisor in the form of . 
so 
.
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