Use the remainder theorem to determine if the given binomial is a factor of f(x)

Question

*please show me all steps that lead to the answer*

f(x)= x^3 - 4x^3 - 75x + 300; x - 5√3

Answer 1

then x=5*Sqrt(3) is a solution IF x - 5*sqrt(3) is a factor

the first term

5*sqrt(3) , when cubed, is 125*3*sqrt(3) = 375*sqrt(3)

second term is (assuming it is quadratic, not cubic like you have in the problem)

-4 * 5*sqrt(3) * 5*sqrt(3) = -300

the linear term is

-75*3*sqrt(3) = -225*sqrt(3)

the total of these including the 300 is not zero, so no

it is not a solution.