Correctness of my equation relative to the standard given in the text

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GOPgabe
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Homework Statement



Given a polynomial P(x) and a divisor D(x), divide P(x) by D(x) and return the answer in the form P(x)/D(x) = Q(x) + R(x)/D(x)

In this case: P(x) = 4x^2 - 3x - 7
D(x) = 2x -1

Homework Equations



The one given above

The Attempt at a Solution



I solved the problem using synthetic division and ascertained: P(x)/D(x) = 2x - (x + 7)/(2x - 1)

It's part of a summer engineering program. The TA, however, counted this wrong. Could somebody tell me what the heck the problem with it is? I mean, I checked with wolfram, and evidently this is right. But... I guess not! Help is much appreciated. :)
 
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The degree of R(x) has to be smaller than the degree of D(x). Since the degree of D(x) is 1, then R(x) has to be a constant.

Also, how did you use synthetic division for this problem? Synthetic division is normally used when D(x) is in the form x - c (c being a number).
 
Your "remainder", (-x- 7)/(2x- 1) can be further divided: -(1/2)- (13/2)/(2x-1)
 
That looks absolutely terrible in terms of written form, but alright. I thought R(x) had to be a function containing x. I see now. Thanks. Oh and sorry i meant long division, I posted that around 1 last night. Haha
 
GOPgabe said:
That looks absolutely terrible in terms of written form, but alright. I thought R(x) had to be a function containing x. I see now. Thanks. Oh and sorry i meant long division, I posted that around 1 last night. Haha

Remember f(x) = 4 is a perfectly valid function in terms of x. Just because the function notation has a variable in it does not mean it HAS to be in the equation just like our constant function or even f(x) = y.

Also the thinking behind the remainder comes from number division. Say you are dividing 10 by 3. You wouldn't say that 3 goes into 10 twice remainder 4 would you? You don't want your remained to be bigger than your divisor. In this case 3 can go into 10 one more time can't it?

Similarly with polynomials 2x - 1 can go into -x - 7 one more time. It goes in -1/2 more times.