SOLUTION: I've had a go at this sequence of questions and come up with some answers, the thing is, I'm not sure that it's correct, please have a look and advise me if you have the time. Pro

Question 1031087: I've had a go at this sequence of questions and come up with some answers, the thing is, I'm not sure that it's correct, please have a look and advise me if you have the time.
Problem(s);
i Determine the remainder when 9 x^5-4 x^4 is divided by 3 x-1
ii Show using the factor theorem the 2x -1 is a factor of 2x^4- x3 -6x^2 + 5x -1 and hence express
2x^4- x3 -6x^2 + 5x -1 as a product of a linear and cubic factor.
this is my go at the first bit:
9 x^5-4 x^4 = (3 x^4-x^3/3-x^2/9-x/27-1/81) � (3 x-1)+-1/81
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
(i)

Do some factoring of the dividend first.

------but do you want to go this way, or do you want to entire dividend including the degrees of x with coefficients of 0?

Here is the polynomial division using divisor .


              3x^4    -(x^3)/3  -(1/9)x^2          -(1/27)x     (1/72)
        _________________________________________________________________________
3x-1    |     9x^5    -4x^4    0x^3                   0x^2       0x       
        | 
        |     9x^5    -3x^4
          -------------------
              0       -x^4     0x^3
                      -x^4     x^3/3
                    -----------------
                       0    -(1/3)x^3  0x^2
                            -(1/3)x^3  (1/9)x^2
                          ----------------------
                               0      -(1/9)x^2   0x
                                      -(1/9)x^2  -(1/27)x
                                     --------------------
                                        0       (1/27)x         0
                                                (1/27)x      -(1/72)
                                               ---------------------
                                                  0         (1/72)

According to that polynomial long division, the quotient INCLUDING remainder is and the quotient including the meaning for the remainder is

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