Question 389687
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dividing (3x^4-3x^3-6x-10)/(x-2) by using long division
          3x^3 + 3x^2 + 6x +6   Remainder = 2
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x-2 |    3x^4  -3x^3  -6x-10
      - (3x^4 - 6x^3)
       ---------------
                3x^3   
             - (3x^3 - 6x^2)
                --------------
                        6x^2 -6x
                      -(6x^2 -12x)
                          --------
                               6x -10
                             -(6x -12)
                              --------
                                   2
dividing (4x^4-12x^3-48x-60)/(x-4)done in similar fashion resulting in
4x^3 + 4x^2 + 16x + 16  Remainder = 4

As to: Using substitution to determine if an x value results in P(x) = 0
simply use that value of x in the function:
P(1)=3x^4-10x^3-29x^2+16x+20 = 3 -10 -29 + 16 + 20 = (29-29)= 0

As to using substitution to determine whether x-3 is a factor of 
4x^4-9x^3-109x^2+225x+225...(x-3) is a factor only if f(3) = 0
f(x) =4x^4-9x^3-109x^2+225x+225
f(3) = 4*81 - 9*27 - 109*9 + 255*3 + 225 = (1224 - 1224) = 0  (x-3) is a factor