The product of both values of x for which 2003^x^2+2x-35 =1 is

A. -2
B. 2
C. -35
D. 35

I will assume you mean

2003^(x^2 + 2x - 35) = 1
then
2003^(x^2 + 2x - 35) = 2003^0

thus: x^2 + 2x - 35 = 0
(x+7)(x-5) = 0
x = -7 or x = 5

and the product of those two x's is -35