Difference between revisions of "Remainder Theorem"
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<cmath>p(a) = q(a) \cdot (a - a) + r(a)</cmath> | <cmath>p(a) = q(a) \cdot (a - a) + r(a)</cmath> | ||
<cmath>p(a) = q(a) \cdot 0 + r(a)</cmath> | <cmath>p(a) = q(a) \cdot 0 + r(a)</cmath> | ||
− | < | + | <cmath>p(a) = r(a)</cmath> |
==Examples== | ==Examples== |
Revision as of 10:47, 20 May 2018
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 .
Proof
Let , where is the polynomial, is the divisor, is the quotient, and is the remainder. This equation can be rewritten as If , then substituting for results in
Examples
Introductory
- 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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