Final answer:
The zeros of the function f(x) are x = 7, x = -4, and x = 1.
Step-by-step explanation:
To find the zeros of the function f(x), we set f(x) equal to zero and solve for x. Given that f(7) = 0, we substitute 7 for x in the function and solve for the zeros.
f(x) = x^3 - 4x^2 - 25x + 28
f(7) = 7^3 - 4(7)^2 - 25(7) + 28
0 = 343 - 196 - 175 + 28
0 = 0
The equation holds true for x = 7, which means 7 is a zero of the function. To find the other zeros, we can divide the function by (x - 7) to get the remaining polynomial.
(x^3 - 4x^2 - 25x + 28) / (x - 7) = x^2 + 3x - 4
Now we can factor the remaining polynomial, x^2 + 3x - 4, to find the other zeros.
x^2 + 3x - 4 = (x + 4)(x - 1)
Therefore, the zeros of the function f(x) are x = 7, x = -4, and x = 1.