If f(x)=6x^3 - ax^2 + bx + c when a, b and c are constant when f(x) is divided by x^2 - 4 the remainder is 23x - 26. When f(x) divided by (x +3) the remainder is -220. Find:

Question

(A) the value of a, b and c
(B) the solution of the equation f
(x)=0

Answer 1

A little division shows that

6x^3-ax^2+bx+c / (x+4)
has a remainder of -16a-4b+c-384

6x^3-ax^2+bx+c/(x^2-4)
has a remainder of (b+24)x+c-4a

So,

-16a-4b+c-384 = -220
b+24 = 23
c-4a = -26

solve those and you get

f(x) = 6x^3 + 31/2 x^2 - x - 88

You can verify the remainders for yourself.

Answer 2

thank you steve! But how to find the value of a and c?