Tutor could you please help me with this long division? 
Using long division divide 7x^3 -3x^2 -4x+5 divided by 7x -1 
Thank you for your help 
I started by doing this: 7x-1/7x^3x^2-4x+5/-7x/x^2

No you begin with this

      ___________________ 
7x - 1)7x³ - 3x² - 4x + 5

Then you mentally divide the 7x into the 7x³ and get x²,
so you write x² above the top line:

              x²
      ___________________ 
7x - 1)7x³ - 3x² - 4x + 5

Perhaps you are accustomed to writing the quotient out
to the right, but it's the same procedure whether you
write it ate the top or at the right.

Now mentally multiply the x² by the -1 and get -x², so
you write - x² under the - 3x²

              x²
      ___________________  
7x - 1)7x³ - 3x² - 4x + 5
           -  x²

Now mentally multiply the x² by the 7x and get 7x³, so
you write 7x³ under the 7x³:

              x² 
      ___________________ 
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²

Now you draw a line at the bottom and subtract vertically.
Be sure to mentally change the sign of the lower number
and add.  -3x²-(-x²) = -3x²+x² = -2x² so write that
below the line.  The 7x²-(7x³) = 0 so you do not write
anything under the line below the 7x³'s:

              x²
      ___________________ 
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
       _________
            -2x²

Now we bring down the - 4x

              x² 
      ___________________
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
       _________
            -2x² - 4x

Now we divide the 7x into the -2x² and get the fraction
-x.  (Are you sure you copied it right?)

So we write x at the top to the right of the x².

              x² -x
      ___________________ 
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
       _________
            -2x² - 4x

Now we multiply the -x by the -1 and get + x,
so we write that underneath the - 4x:

              x² -x
      ___________________
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
       _________
            -2x² - 4x
                 + x

Now we multiply the -x by the 7x and get -2x²,
so we write that underneath the -2x²

              x² -x
      ___________________
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
       _________
            -2x² - 4x
            -2x² + x

Now we draw a line at the bottom and subtract:

-4x - (+x = -4x - x = -x. So
we write that below the line:

              x² -x
      ___________________
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
       _________
            -2x² - 4x
            -2x² + x
            _________
                 -x            

The -2x-(-2x) = -2x+2x = 0 so we do not write
anything under the line below the -2x²'s:

Now we bring down the + 5

              x² -x     
      ___________________ 
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
       _________
            -2x² - 4x
            -2x² + x
            _________
                 -x + 5
   
Next we divide the 7x into the -x and get -,
so we write that at the top:

              x² -x -      
      ___________________ 
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
            -2x² - 4x
            -2x² + x
            _________
                 -x + 5


Now we multiply the - by the - 1 and get + 
and write that under the 5:

              x² -x -      
      ___________________ 
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
       _________
            -2x² - 4x
            -2x² + x
            _________
                 -x + 5
                      +

Now we multiply the - by the 7x and get -x
so write that to the left of the + 

              x² -x -      
      ___________________ 
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
       _________
            -2x² - 4x
            -2x² + x
            _________
                 -x + 5
                 -x +

Now we draw a line at the bottom and subtract:

5 - (+) = 5 -  = 

And we write that at the bottom.  Now we have finished
the long division (whew!!!).   
              
              x² -x -      
      ____________________ 
7x - 1)7x³ - 3x² - 4x + 5
       7x³ -  x²
       _________
            -2x² - 4x
            -2x² + x
            _________
                 -x + 5
                 -x +
                 __________
                       


So now we write the answer in the form

 +  or

x² -x -  + 

We can simplify the last fraction by multiplying
top and bottom by 49, so the final answer is:

x² -x -  + 

Your teacher was MEAN to give you that problem!

J

Edwin