SOLUTION: Divide: x^2-2x-35 _________= ?????? x+5

 x²-2x-35
——————————
   x+5
   
There are 3 ways to do it, depending on
where you are in the book.
---------------------------------------
Method 1:  Long division:

            x -  7
x + 5)x² - 2x - 35
      x² + 5x
          -7x - 35
          -7x - 35
                 0

So the answer is the quotient x - 7
----------------------------------------
Method 2:  Synthetic division:
     _________ 
   -5|1 -2 -35
     |  -5  35
      1 -7   0

So the answer is x - 7
----------------------------------------
Method 3:  Factoring and canceling:

 x²-2x-35
——————————
   x+5

 Factor the trinomial numerator.
 x²-2x-35
(x  )(x  )
Think of two integers whose product is 35
and whose difference is 2.  They are 7 and 5
(x 7)(x 5)
Then since the 7 is larger it gets the same
sign as the -2x or -, and the 5 gets the
opposite sign, +
(x-7)(x+5)

So the fraction

 x²-2x-35
——————————
   x+5

becomes 

 (x-7)(x+5)
————————————
    x+5
 
Now cancel the x+5 in the
denominator into the (x+5)
 in the numerator:

        1
 (x-7)(x+5)
————————————
    x+5
     1

This leaves 

    (x-7)

or just

    x - 7

Edwin