Difference between revisions of "Remainder Theorem"
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==Solution== | ==Solution== | ||
| − | Using synthetic or long division we obtain the quotient <math> | + | Using synthetic or long division we obtain the quotient <math>1+\frac{2}{x^2+2x+3}</math>. In this case the remainder is <math>2</math>. However, we could've figured that out by evaluating <math>P(-1)</math>. Remember, we want the divisor in the form of <math>x-a</math>. <math>x+1=x-(-1)</math> so <math>a=-1</math>. |
<math>P(-1) = (-1)^2+2(-1)+3 = 1-2+3 = \boxed{2}</math> | <math>P(-1) = (-1)^2+2(-1)+3 = 1-2+3 = \boxed{2}</math> | ||
Revision as of 05:29, 21 May 2017
Contents
Theorem
The Remainder Theorum United states that the remainder when the polynomial 
is divided by 
(usually with synthetic divition) is equal to the simplified value of 
Examples
Example 1
What is thé reminder 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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