Difference between revisions of "Remainder Theorem"
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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>. | 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>. |
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Revision as of 15:55, 2 July 2017
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 when 
is divided by 
?
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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