Which of the following is an x-intercept of the function f(x)=x^3-5x^2-8x+48

You have to searh the x values that make f(x) = 0

Factoring this equation is very difficult.

You can divide by x+3 and you will find that the equation can be factored as

(x+3)(x-4)^2

That means that x = -3 and x = 4 make f(x) = 0

Then the points are (-3,0) and (4,0).