Difference between revisions of "Polynomial Remainder Theorem"
(Created page with "==Statement== The Polynomial Remainder Theorem states that for <math>\frac{f(x)}{x-a}</math> the remainder is <math>f(a)</math> ==Proof== Assuming <math>r</math>=re...") |
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==Proof== | ==Proof== | ||
| − | Assuming <math>r</math>=remainder <math>q(x)</math>=quotient and <math>f(x)</math> as a polynomial: | + | Assuming <math>r</math> = remainder <math>q(x)</math> = quotient and <math>f(x)</math> as a polynomial: |
<math>f(x)=q(x)(x-a)+r</math> | <math>f(x)=q(x)(x-a)+r</math> | ||
Revision as of 19:36, 12 February 2018
Statement
The Polynomial Remainder Theorem states that for 
the remainder is 
Proof
Assuming 
= remainder 
= quotient and 
as a polynomial:
If we plug in 
into the polynomial and 
(Do not plug into . Assume as only a variable for quotient) we get:
