Factorise:

The given expression is $3+23 z-8 z^{2}$.

Find two numbers that follow the conditions given below:

Sum $=23$

Product $=3 \times-8=-24$

Clearly, the numbers are 24 and $-1$.

$3+23 z-8 z^{2}=3+24 z-z-8 z^{2}$

$=3(1+8 z)-z(1+8 z)$

$=(1+8 z)(3-z)$