Hello,

it's me again. (I started this post but suddenly it has vanished without a trace... )

To #13 and #14: I don't know the difference between long division and synthetic division (that has nothing to do with my limited kowledge of Math but with the incompleteness of my dictionary!) I'll do both problems the same way - and hope that you can use my reply nevertheless:

to #13:

Code:

(3x^3 + x^2 + 4x - 5)÷(3x-2) = x^2+x+2, remainder (-1)
-(3x^3 -2x^2)
--------------
3x^2 + 4x
-(3x^2 - 2x)
------------
6x - 5
-(6x - 4)
--------
-1

I've learned that the result is:

$\displaystyle (3x^3+x^2+4x-5)\div (3x-2)=x^2+x+2-\frac{1}{3x-2}$

to #14:

Code:

(x^4 - 3x^3 - 2x^2 + 1)÷(x-3) = x^3-2x-6, remainder -17
-(x^4 - 3x^3)
--------------
-2x^2 + 1
-(-2x^2+6x)
-------------
-6x + 1
-(-6x + 18)
-----------
-17

That means:

$\displaystyle (x^4-3x^3-2x^2+1) \div (x-3)=x^3-2x-6-\frac{17}{x-3}$

EB