Characteristic Polymonmial 4x4 Matrix

Question

I have to find the characteristic polynomial to find Jordan normal form. I chose to solve this via column expansion on the first determinant, and then row expansion in the inner determinant. But something has clearly went wrong, as I know my answer is incorrect. Please help me figure this out, I am stuck. Maybe the way I expand the determinant is wrong?

I know my final answer is wrong. The correct answer is:

$(x-1)^4$

And here is the question:

Answer 1

In your row expansion, your second term should be

$$-(-3)\det{\begin{pmatrix} -2& 13\\ -1& (8-\lambda) \end{pmatrix}}$$