# Math Help - Factor theorem to find variable

1. ## Factor theorem to find variable

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.

2. ## Re: Factor theorem to find variable

The remainder of $\frac{f(x)}{x+2}$ is $f(-2)$, or $4 - 2k$

The remainder of $\frac{f(x)}{x-2}$ is $f(2)$, or $20 + 2k$

4-2k is twice that of 20+k, so $4-2k = 2(20+2k) \Rightarrow k = -6$.