Originally Posted by

**topsquark** Well, f(x) is divisible by $\displaystyle x^2 - 2x = x(x - 2)$ so we know f(x) is divisible by x. Thus c = 0 immediately. Consider then

$\displaystyle f(x) = ax^3 - (a + 3b)x^2 + 2bx$

From the original statement (divisible by x(x - 2)), we get

$\displaystyle f(2) = a(2)^3 - (a + 3b)(2)^2 + 2b(2) = 0$

Call

$\displaystyle f(1) = a(1)^3 - (a + 3b)(1)^2 + 2b(1) = d$

Then we know that

$\displaystyle f(-1) = a(-1)^3 - (a + 3b)(-1)^2 + 2b(-1) = d - 8$

Three equations, three unknowns.

-Dan