SOLUTION: Determine the remainder when f(x)=x^3-5x^2+6 is divided by x-3

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Question 1110635: Determine the remainder when f(x)=x^3-5x^2+6 is divided by x-3
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
According to the Remainder theorem, the remainder under the question is equal to  


    f(3) = 3%5E3+-5%2A3%5E2+%2B+6,


which you can easily calculate on your own.


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   Theorem   (the remainder theorem)
   1. The remainder of division the polynomial  f%28x%29  by the binomial  x-a  is equal to the value  f%28a%29  of the polynomial.
   2. The binomial  x-a  divides the polynomial  f%28x%29  if and only if the value of  a  is the root of the polynomial  f%28x%29,  i.e.  f%28a%29+=+0.
   3. The binomial  x-a  factors the polynomial  f%28x%29  if and only if the value of  a  is the root of the polynomial  f%28x%29,  i.e.  f%28a%29+=+0.


See the lessons
    - Divisibility of polynomial f(x) by binomial (x-a) and the Remainder theorem
    - Solved problems on the Remainder thoerem
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.