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For what value of k is the remainder 0 when the function g(x)=-3xk^3+kx-2 is divided by (x-2)?

 Jul 23, 2021
 #1
avatar+121055 
+3

 

2  [  (-3k^3  + k)  -  2   ]

                           - 6k^3 + 2k

    _______________________

      -3k^3  + k       -6k^3  + 2k - 2

 

So

 

-6k^3 + 2k  - 2  = 0         divide through by  -2

 

3k^3  - k  + 1    =   0

 

Solving this  with a CAS, we  get that

 

k ≈  -.85138

 

 

cool cool cool

 Jul 23, 2021
 #2
avatar+34388 
+3

Similarly, if the result is 0 when divided by (x-2) , then x = 2 is a root

sub in x = 2

 

-6 k^3 +2k - 2 = 0   simplify

3k^3 - k + 1 = 0

 

then the answer is  k =  -0.85138 as Chris found   ...... 

 Jul 23, 2021

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