I'm realy stuck to the attached question I know how to do synthetic and long division, and that the remainder is just the value of the function after plugging in x.
help would be greatly appreciated. thanks.
The remainder of $\displaystyle \frac{f(x)}{x+2}$ is $\displaystyle f(-2)$, or $\displaystyle 4 - 2k$
The remainder of $\displaystyle \frac{f(x)}{x-2}$ is $\displaystyle f(2)$, or $\displaystyle 20 + 2k$
4-2k is twice that of 20+k, so $\displaystyle 4-2k = 2(20+2k) \Rightarrow k = -6$.