Remainder Theorem: Difference between revisions
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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> | ||
==What | =Examples= | ||
==Example 1== | |||
What is the remainder 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>x=-1</math>. | |||
<math>P(-1) = (-1)^2+2(-1)+3 = 1-2+3 = \boxed{2}</math> | |||
Revision as of 11:49, 20 November 2011
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 
.
