How can I divide a polynomial by (x+k) using synthetic division?

[markosheehan]

i am trying to divide x^3+(1-k^2)x+k by (x+k) but i can't do this can you show me how to.

 

[MarkFL]

I would use synthetic division here:

$$\begin{array}{c|rr}& 1 & 0 & 1-k^2 & k \\ -k & & -k & k^2 & -k \\ \hline & 1 & -k & 1 & 0 \end{array}$$

Thus, we may state:

$$x^3+(1-k^2)x+k=(x+k)(x^2-kx+1)$$