We want to simplify
(12zΒ² + 25z + 12)/(3zΒ² - 2z - 8)
Note that
12zΒ² + 25z + 12 = (4z + 3)(3z + 4)
3zΒ² - 2z - 8 = (z - 2)(3z + 4)
Therefore
[tex] \frac{12z^{2}+25z+12}{3z^{2}-2z-8} = \frac{(4z+3)(3z+4)}{(z-2)(3z+4)}= \frac{4z+3}{z-2} [/tex]
Answer:Β (4z+3)(z-2)
In words:
4z plus 3 over z minus 2
