Given

z² – 12z – 45

Now first find the numbers whose-

Sum = - 12 and

Product = - 45

Required numbers are 15 and 3,

So we get;

z² – 12z – 45

= z² – 15z + 3z - 45

= z(z – 15) + 3(z – 15)

= (z – 15)(z + 3)