Difference between revisions of "Remainder Theorem"
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What is the remainder in <math>\frac{x^2+2x+3}{x+1}</math>? | What is the remainder in <math>\frac{x^2+2x+3}{x+1}</math>? | ||
==Solution== | ==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> | + | 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> | <math>P(-1) = (-1)^2+2(-1)+3 = 1-2+3 = \boxed{2}</math> |
Revision as of 07:07, 11 December 2011
Contents
[hide]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 .