One root of f(x)=x^3-4x^2-20x+48 is x = 6. what are all the factors of the function? use the remainder theorem.

a.(x + 6)(x + 8)
b.(x – 6)(x – 8)
c.(x – 2)(x + 4)(x – 6)
d.(x + 2)(x – 4)(x + 6)

If one root is x = 6, then this polynomial is divisible by: x - 6.
( x³ - 4 x² - 20 x + 48 ) : ( x - 6 ) = x² + 2 x - 8
- x³ + 6x²

         2 x² - 20 x
        -2x² + 12 x
      
                 - 8 x + 48
                   8 x - 48
              
After that : x²+ 2 x - 8 = x² + 4 x - 2 x - 8 = x * ( x + 4 ) - 2 * ( x + 4 ) =
= ( x + 4 ) ( x - 2 )
C )  ( x - 2 ) ( x + 4 ) ( x - 6 )

Your answer will be