Factorise:

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

Find two numbers that follow the conditions given below:

Sum $=10$

Product $=3 \times 8=24$

Clearly, the numbers are 6 and 4 .

$3 x^{2}+10 x+8=3 x^{2}+10 x+8$

$=3 x^{2}+6 x+4 x+8$

$=3 x(x+2)+4(x+2)$

$=(x+2)(3 x+4)$