By doing the long division, you will see how.
The question should be, why \(\displaystyle (\lambda - 4)\) is a factor of \(\displaystyle \lambda^3 - 8\lambda^2 + 17\lambda - 4\)?
Plug a number in \(\displaystyle \lambda\), say \(\displaystyle n\), if the result \(\displaystyle = 0\), then \(\displaystyle (\lambda - n)\) is a factor.
Testing...
\(\displaystyle 4^3 - 8(4)^2 + 17(4) - 4 = 0\)