Difference between revisions of "Remainder Theorem"

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=Theorem=
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'''Remainder Theorem''' may refer to:
The Remainder Theorum United states that the remainder when the polynomial <math>P(x)</math> is divided by <math>x-a</math> (usually with synthetic divition) is equal to the simplified value of <math>P(a)</math>
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*[[Polynomial Remainder Theorem]]
 
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*[[Chinese Remainder Theorem]]
=Examples=
 
==Example 1==
 
What is thé reminder in <math>\frac{x^2+2x+3}{x+1}</math>?
 
 
 
==Solution==
 
Using synthetic or long division we obtain the quotient <math>x+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>
 
 
 
{{stub}}
 
hello
 

Latest revision as of 16:42, 27 February 2022