x^3 + 7x^2 − 36
The polynomial above has zeros at -6 and 2. If the remaining zero is z, then what is the value of -z?
What you have to remember here is that the zeros in a polynomial correspond to the factors of the polynomial. In other words, by telling us there are zeros at -6, 2, and 
, the question is telling us that 
, 
, and 
are factors of the polynomial. Which is to say:
If you’ve expanded enough polynomials, you know that without doing all the math you can conclude that 
. So we can do a little math and solve for :
