If possible, please convert these words to the equivalent symbolic equation:
12z^2 - 25z + 12
-------------------------
3z^2 + 2z - 8
It's possible that the numerator and the denominator share a common factor. Thus, the first thing we should do here is try to factor the simpler 3z^2 + 2z - 8:
(3z - 4)(z + 2 ).
Next, determine whether either of these two factors is also a factor of
12z^2 - 25z + 12. Borrowing the factor (3z-4) and noting that 4/3 would be the corresponding divisor in synthetic division, I found that there was a zero remainder, which tells us that (3z - 4) actually is a factor of 12z^2 - 25z + 12.
Thus, the original expression,
12z^2 - 25z + 12 (3z-4)(4z-3)
------------------------- factors into -------------------------------
3z^2 + 2z - 8 (3z-4)(z+2)
The common factor here is (3z-4). Cancelling that, we get:
4z-3
------- which is the final answer, the quotient reduced to lowest terms.
z+2
