Question: Factorise:
z2 − 12z − 45
Solution:
The given expression is $z^{2}-12 z-45$.
Find two numbers that follow the conditions given below:
Sum $=-12$
Product $=-45$
Clearly, the numbers are $-15$ and 3 .
$z^{2}-12 z-45=z^{2}-15 z+3 z-45$
$=z(z-15)+3(z-15)$
$=(z-15)(z+3)$
