The given function is
f(x) = x^2 + 2x - 35
To find the zeros, we would equate it to zero and factorize. It becomes
x^2 + 2x - 35 = 0
This is a quadratic equation. We would solve by applying the method of factorization. The first step is to multiply x^2 with - 35. It becomes - 35x^2. We would find two terms such that their sum or difference is 2x and their product is - 35x^2. The terms are 7x and - 5x. By replacing 2x with 7x - 5x, we have
x^2 + 7x - 5x - 35 = 0
We would factorize by grouping. It becomes
x(x + 7) - 5(x + 7) = 0
Since (x + 7) is common, it becomes
(x - 5)(x + 7) = 0
x - 5 = 0, x + 7 = 0
x = 5, x = - 7
The zeros of the function are x = 5, x = - 7