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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)
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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)
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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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