Real Zeros of Polynomial Function...3

Section 2.5
Question 92

Please, work out 92 as a guide for me to do the rest.

 

f(z)=12z^3-4z^2-27z+9

f(z)=12z^3+14z^2-18z^2-6z-21z+9

f(z)=(12z^3-18z^2)+(14z^2 -21z)-(6z-9)

f(z)=6z^2(2z-3)+7z(2z -3)-3(2z-3)

f(z) = (2z - 3) (6z^2 + 7z - 3)

f(z) = (2z - 3) (6z^2 -2z+ 9z - 3)

f(z) = (2z - 3) ((6z^2 + 9z)-(2z + 3))

f(z) = (2z - 3) (3z(2z + 3)-(2z + 3))

f(z) = (2z - 3) (2z + 3) (3z - 1)

 

Thanks again. I can take it from here.