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| =Theorem=
| | '''Remainder Theorem''' may refer to: |
| 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>
| | *[[Polynomial Remainder Theorem]] |
| | | *[[Chinese Remainder Theorem]] |
| =Examples=
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| ==Example 1==
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| What is the remainder in <math>\frac{x^2+2x+3}{x+1}</math>?
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| ==Solution==
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| 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>.
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| <math>P(-1) = (-1)^2+2(-1)+3 = 1-2+3 = \boxed{2}</math>
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Latest revision as of 15:42, 27 February 2022
Remainder Theorem may refer to:
