SOLUTION: Hello to all! I have been tackling this problem for the past 4 hours, and sadly with no luck! The function f(x)=x^3+3x^2+kx-4. The remainder when f(x) is divided by (x+2) is tri

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello to all! I have been tackling this problem for the past 4 hours, and sadly with no luck! The function f(x)=x^3+3x^2+kx-4. The remainder when f(x) is divided by (x+2) is tri      Log On


   

Question 1153869: Hello to all! I have been tackling this problem for the past 4 hours, and sadly with no luck!
The function f(x)=x^3+3x^2+kx-4. The remainder when f(x) is divided by (x+2) is triple the remainder when f(x) is divided by (x-2). Determine the value of k.
At first I used (x-2), and let the value for x=2. Input 2 into the equation to find the value of K which i get -8. However when I try to do the division with both values to find the remainder to confirm my answer, everything goes haywire! Please help me :(
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Thanks for saying what you did on the problem... but I don't understand it.

The remainder when a polynomial f(x) is divided by (x-a) is equal to f(a).

The remainder when the given polynomial is divided by (x+2) (that is, (x-(-2)) is f(-2):

%28-2%29%5E3%2B3%28-2%29%5E2%2Bk%28-2%29-4+=+-8%2B12-2k-4+=+-2k

The remainder when the given polynomial is divided by (x-2) is f(2):

%282%29%5E3%2B3%282%29%5E2%2Bk%282%29-4+=+8%2B12%2B2k-4+=+2k%2B16

The first remainder is 3 times the second:

-2k+=+3%282k%2B16%29

Finish from there with basic algebra....

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

The key to solving this problem is the Remainder theorem, as tutor @greenestamps showed to you in his post.

If you do not know this theorem,  you will  NEVER  solve this problem.
You even will never know how and where to start (!)

But,  in opposite,  if you  DO  KNOW  the theorem,  then you will be able to solve this
and hundreds other similar problems,  that otherwise,  you think,  seem to be unsolvable,  from the first glance  (!)


To learn about the Remainder theorem and to see many other nice problems,  solved with it,  look into 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.