SOLUTION: how can i find the answer by using long division? (x^2+1/2X-3/16)/(X+3/4)

Question 72924: how can i find the answer by using long division?
(x^2+1/2X-3/16)/(X+3/4)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

     _________________ 
x+3/4| x^2+1/2x-3/16

Set the division problem in this form. We are looking for a number that multiplies by x to get x^2, this number is x (x*x=x^2)

     __x______________ 
x+3/4| x^2+1/2x-3/16

Multiply x by (x+3/4) and place the result under x^2+1/2x-3/16

     __x______________ 
x+3/4| x^2+1/2x-3/16
     -(x^2+3/4x)

Subtract the result (x^2+3/4x) from x^2+1/2x-3/16

     __x______________ 
x+3/4| x^2+1/2x-3/16
     -(x^2+3/4x)                  
     -----------------
      0x^2-1/4x-3/16         (remember distribute the negative and bring down -3/16)

Now we're looking for a value that multiplies by x to get -1/4x (which is -1/4) this is placed over the 1/2x in the quotient

     __x__-1/4____________ 
x+3/4| x^2+1/2x-3/16
     -(x^2+3/4x)                  
     -----------------
      0x^2-1/4x-3/16

Multiply -1/4 by (x+3/4) and place it under -1/4x-3/16

     __x__-1/4____________ 
x+3/4| x^2+1/2x-3/16
     -(x^2+3/4x)                  
     -----------------
      0x^2-1/4x-3/16   
         -(1/4x-3/16)
        --------------
           0x+0             Notice how you got a remainder 0

A remainder of 0 shows that (x+3/4) is a factor of (x^2+1/2X-3/16) (its like saying 2 is a factor of 6 since there are no remainders leftover).
So the answer is (x-1/4)

Check:
You can plug in 1/4 into (x-1/4) to get (1/4-1/4)=0 and plug in 1/4 into (x^2+1/2X-3/16) to get 0 also (they should be equal).

You can use synthetic division (if you are unfamiliar with this technique look up http://www.purplemath.com/modules/synthdiv.htm or google "synthetic division")

-3/4| 1   1/2    -3/16
    |
    |____-3/4_____3/16_____ 
      1  -1/4      0

The answer is (x-1/4)
So this shows that x=-3/4 is a zero and x=1/4 is also a zero. Synthetic division is a much faster way to get to the same answer.
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