Question

What is the simplified form of the quantity 12 z-squared plus 25z plus 12 over the quantity 3 z-squared minus 2z minus 8 ?

4z plus 3 over z plus 2
4z minus 3 over z plus
4z plus 3 over z minus
4z minus 3 over z minus 2

Answer 1

We want to simplify
(12z² + 25z + 12)/(3z² - 2z - 8)

Note that
12z² + 25z + 12 = (4z + 3)(3z + 4)
3z² - 2z - 8 = (z - 2)(3z + 4)

Therefore

`(12z^(2)+25z+12)/(3z^(2)-2z-8) = ((4z+3)(3z+4))/((z-2)(3z+4))= (4z+3)/(z-2)`

Answer: (4z+3)(z-2)
In words:
4z plus 3 over z minus 2