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Polynomial Division and Factorization - Proof of Remainder Theorem - Exercise 4

Given f(x) is a polynomial that is divided by g(x) = x - c and the resulting quotient is Q(x) and the resulting remainder is r. Show that f(c) = r.  Hint: Apply the Division Algorithm to write f(x) as a product plus a remainder. Then let x=c.  No further justification is needed, but be able to explain your work.
 

STATEMENT JUSTIFICATION
f(x) D(x) results in a quotient of Q(x) and a remainder of r.

 

 

 

 

 

 

 

 

 

 

Application of Division Algorithm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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