Factorise:

The given expression is $3 z^{2}-10 z+8$.

Find two numbers that follow the conditions given below:

Sum $=-10$

Product $=3 \times 8=24$

Clearly, the numbers are $-6$ and $-4$.

$3 z^{2}-10 z+8=3 z^{2}-6 z-4 z+8$

$=3 z(z-2)-4(z-2)$

$=(3 z-4)(z-2)$