If x+10 was a factor of f(x), then x = -10 would lead to f(x) = 0. This is because we set x+10 equal to zero and solve for x.
Plug x = -10 into f(x). Let's see what result we get. If the result is 0, then x+10 is a factor.
f(x) = x^3 - 75x + 250
f(-10) = (-10)^3 - 75(-10) + 250
f(-10) = -1000 + 750 + 250
f(-10) = -250 + 250
f(-10) = 0
Answer: Yes x+10 is a factor of f(x)
