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

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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

or