What are the zeros of the function? g(x)=x^2−x−72

and

The "zeros" or "roots" are the x values that make g(x) = 0.
Factor the expression and use the zero product property.

g(x) = 0
x^2 - x - 72 = 0
(x - 9)(x + 8) = 0 ... ** see note below **
x - 9 = 0 or x + 8 = 0
x = 9 or x = -8

The two answers are: 9 and -8

Note: you need to find two numbers that multiply to -72 (last term of the given expression) and add to -1 (middle coefficient of the given expression). These two numbers are -9 and 8. Note how
-9 plus 8 = -1
-9 times 8 = -72
So that's why x^2 - x - 72 factors to (x-9)(x+8)