z² + 12z + 27

Now first find the numbers whose-

Sum = 12 and

Product = 27

Required numbers are 9 and 3,

So we get;

z² + 12z + 27

= z² + 9z + 3z + 27

= z(z + 9) + 3(z + 9)

= (z + 9)(z + 3)