Question 1170859
.
<pre>

In accordance with the Remainder theorem,  the given part means that the given polynomial has the roots of 1, -2 and 2.


So we write these three equations expressing this fact

    2A*1^4    - B*1^3    - C*1     - 16 = 0

    2A*(-2)^4 - B*(-2)^3 - C*(-2)  - 16 = 0

    2A*2^4    - B*2^3    - C*2     - 16 = 0


or

    2A -  B -  C = 16    (1)

   32A + 8B + 2C = 16    (2)

   32A - 8B - 2C = 16    (3)


Adding equations (2) and (3), you get

   64A           = 32,   which implies  A = {{{32/64}}} = 0.5.


Then from (1) and (2), substituting A = 0.5 there, you get

     B +  C = -15        (4)

    8B + 2C =   0        (5)


Expressing  B = -15 - C  from (4)  and substituting it to (5), you get

    8*(-15 -C) + 2C = 0,    or

    -120 - 8C +  2C = 0

         - 6C = 120

            C = - 20.


Then from equation (4),  B = -15 - (-20) = -15 + 20 = 5.


<U>ANSWER</U>.  A = 0.5;  B = 5,  C = -20.
</pre>

Solved.