SOLUTION: Find the constant C such that the denominator will divide evenly into the numerator. x^4-x^3-3x^2-Cx-3/x-3 Show the solution.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the constant C such that the denominator will divide evenly into the numerator. x^4-x^3-3x^2-Cx-3/x-3 Show the solution.      Log On


   



Question 1186707: Find the constant C such that the denominator will divide evenly into the numerator.
x^4-x^3-3x^2-Cx-3/x-3
Show the solution.

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
If x takes the value of 3, then the condition means the numerator should be 0.

3%5E4%2B3%5E3-3%2A3%5E2-3C-3=0
81%2B27-27-3-3C=0
78=3C
cross%28C=26%29


( sign mistake )

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the constant C such that the denominator will divides evenly into the numerator.
x^4-x^3-3x^2-Cx-3/x-3
~~~~~~~~~~~~~~~~~~~

The linear binomial (x-3) in the denominator divides the polynomial  f(x) = x^4 - x^3 - 3x^2 - Cx - 3  of the numerator evenly 

if and only if  f(3) = 0   (the Remainder Theorem).


From condition  f(3) = 0  find the value of C


    3^4 - 3^3 - 3*3^2  - C*3 - 3 = 0.


It gives


    3C = 3^4 - 3^3 - 3*3^2 - 3 = 81 - 27 - 3*9 - 3 = 24.


Hence,  C = 24/3 = 8.    ANSWER


CHECK.  f(3) = 3^4 - 3^3 - 3*3^2 - 8*3 - 3 = 81 - 27 - 27 - 24 - 3 = 0.

Solved.


////////////


The response by @josgarithmetic,  giving the answer   highlight%28C=26%29   is  INCORRECT.


\\\\\\\\\\\\\


After my noticing, @josgarithmetic fixed his erroneous answer,

but his calculations (starting from the setup equation) remained INCORRECT.


NEVER trust his solutions; ALWAYS avoid his posts, for your safety.

This person makes errors everywhere and always.