Wondering if I crossed all my T's and dotted all my I's with this problem

[mickey222]

is -6h²+3h-18hx+6x-18x²-4

as correct as -6h²-18x²+3h-18hx+6x-4 ?

Something something about "degrees"... Do the higher degrees need to precede the terms with lower degrees?

 

[Deleted member 4993]

is -6h²+3h-18hx+6x-18x²-4

as correct as -6h²-18x²+3h-18hx+6x-4 ?

Something something about "degrees"... Do the higher degrees need to precede the terms with lower degrees?

That is the "convention".

 

[Steven G]

is -6h²+3h-18hx+6x-18x²-4

as correct as -6h²-18x²+3h-18hx+6x-4 ?

Something something about "degrees"... Do the higher degrees need to precede the terms with lower degrees?

Convention or not, what was the instruction for this problem. I am convinced that -6h²+3h-18hx+6x-18x²-4 = -6h²-18x²+3h-18hx+6x-4 but I have no idea if that is the answer to your problem. For example, if they wanted the problem written in standard form as a polynomial in x, then your answer is not correct. It would be -18x² + (6-18h)x + (-6h² + 3h -4

So please post the exact problem.

 

[mickey222]

So please post the exact problem.

Given

, Simplify the following.

1. First I found f(x+h) by plugging x+h into the original function, and I got: 6x³-18x²h-18xh²-6h³+3x²+6xh+3h²-4x-4h-7

2. Then, because I could not simplify that further, I performed f(x+h)-f(x). So I combined the above answer with f(x)-- the original function. That combination looked like this: 6x³-18x²h-18xh²-6h³+3x²+6xh+3h²-4x-4h-7 - (-6x³+3x²-4x-7)
3. The result of that was: -6h³+3h²-18xh²+6xh-18x²h-4h
4. Now, I put that over H: -6h³+3h²-18xh²+6xh-18x²h-4h
H
5. That is supposed to be one long division line, sorry. Then, I factored out a single H from the numerator. I canceled out this H, along with the H in the denominator, and was left with:

-6h²+3h-18xh+6x-18x²-4

 

[Steven G]

Why didn't you give us the exact problem to start off with especially if you wanted us to check your work???

I think that -6h²+3h-18xh+6x-18x²-4 is a perfectly acceptable answer.

Any attempt to change it can cause an error in copying.

 

[Dr.Peterson]

is -6h²+3h-18hx+6x-18x²-4

as correct as -6h²-18x²+3h-18hx+6x-4 ?

Something something about "degrees"... Do the higher degrees need to precede the terms with lower degrees?

I believe you are just asking about the convention for writing polynomials in two variables, not about whether the answer is correct for the unstated problem.

The answer is that, although there is a convention for polynomials in one variable, which some teachers would tell you you must follow in order to get full grades (namely, "descending order by degree"), there is no such universal convention when there are more variables, as here. The answers are equivalent, and neither is more "correct" than the other.

If I were writing this and wanted to format it in a pretty way for publication, I might order the terms as if x were the only variable, and then secondarily order by the degree of h. I would get -18x²-18hx+6x-6h²+3h-4: I put the one x² term first, then the two x terms (in descending order by h), and the three "constant" terms last (in descending order by h). But that is entirely a matter of taste (and of experience with what might be easiest to work with in subsequent steps).

Another convention would be to write terms in descending order by total degree (e.g. terms -6h², -18hx, -18x² all have degree 2 and would come first.

But none of this is required.

 

[mickey222]

\frac{h\left(-6h^2+3h-18xh+6x-18x^2-4\right)}{h}

Why didn't you give us the exact problem to start off with especially if you wanted us to check your work???

I didn't want to ask you guys for that kind of help considering all the help you guys gave me last week. I was reasonably sure I got this one correct-- I was just unsure about the convention about degrees. I provided my work just to show how I got my answer.

 

[Steven G]

I believe you are just asking about the convention for writing polynomials in two variables, not about whether the answer is correct for the unstated problem.

Yes, I understand what you said above completely. The thing is that people make mistakes and we could have checked the entire problem (which I eventually did) just to be sure if it was correct. I also feel that the answer to the OP's original question really depended on knowing the entire problem. For example, if this was a calculus problem where we took the limit as h goes to 0, then the order for h did not matter as all h's will disappear in the end.

 

[mickey222]

I believe you are just asking about the convention for writing polynomials in two variables, not about whether the answer is correct for the unstated problem.

The answer is that, although there is a convention for polynomials in one variable, which some teachers would tell you you must follow in order to get full grades (namely, "descending order by degree"), there is no such universal convention when there are more variables, as here. The answers are equivalent, and neither is more "correct" than the other.

If I were writing this and wanted to format it in a pretty way for publication, I might order the terms as if x were the only variable, and then secondarily order by the degree of h. I would get -18x²-18hx+6x-6h²+3h-4: I put the one x² term first, then the two x terms (in descending order by h), and the three "constant" terms last (in descending order by h). But that is entirely a matter of taste (and of experience with what might be easiest to work with in subsequent steps).

Another convention would be to write terms in descending order by total degree (e.g. terms -6h², -18hx, -18x² all have degree 2 and would come first.

But none of this is required.

Thanks for the thorough answer Dr. P.

 

[mickey222]

Yes, I understand what you said above completely. The thing is that people make mistakes and we could have checked the entire problem (which I eventually did) just to be sure if it was correct. I also feel that the answer to the OP's original question really depended on knowing the entire problem. For example, if this was a calculus problem where we took the limit as h goes to 0, then the order for h did not matter as all h's will disappear in the end.

Understood, thanks for the help, and I'll remember that in the future.