All your examples are grammatically correct.
I haven't collected statistics
but I'd guess "her homework" is most commonly used.
You could certainly say that "her" is not required, as the reader is unlikely to suppose that she does someone else's homework.
I have an intuitive feel that "she does homework every day
" sounds like it's saying that she has a lot of homework, that the emphasis is on the idea that she's doing it every day.
But "she does her homework every day" sounds more like it's emphasizing that she is living up to her responsibilities.
But I'd be hard-pressed to give a logical argument for that interpretation.
Maybe "her" makes it more personal, she's doing the homework assigned to her?
While simply "homework" puts the emphasis on the work itself?
"The homework" would indicate that it is some specific homework.
You wouldn't use it to refer to homework in general.
Like you mean say, "She does the homework from her biology class".
Or, "Did you do the homework
the teacher assigned yesterday?
" But you wouldn't say, "She does the homework every day" to refer to doing homework in general.
ell.stackexchange.com/users/803/Jay
or is the object her required?
I wouldn't call her an object, but rather a pronoun that modifies the object homework .
It's not required for grammatical correctness, but in practice the version with the pronoun has a connotation of all of the subject's homework, while the version without is more indefinite.
She does homework every day.
At least in American usage, one would generally take this to mean that she spends time working on homework, but doesn't necessarily complete all the work.
She does her homework every day.
This generally means that she does all the homework assigned to her, or at least everything she needs to have done for the next day.
The possessive pronoun "her" specifies which homework you're talking about, and the implication is that you mean all of it.
If your mother asks you if you've done your homework and you say "yes," you'll be in trouble if she finds out later that you only completed half of it.
She does the homework every day.
The article
the here makes this version relate to some specific homework, like that for a specific class.
For example: She succeeds in math class because she does the homework every day.
It's worth pointing out that doing your homework often relates to being prepared even for people who aren't students, and in that case you generally mean that the subject is (or isn't) fully prepared, so the possessive pronoun is often used, or an adjective is used to clarify the meaning.
Some examples: To avoid losing money, do your homework before investing in a new company.
She knew he was lying because she did her homework before the deposition.
Do some homework before buying a house
: check prices of recent sales, school quality, etc.
ell.stackexchange.com/users/9737/Caleb
They have different meanings.
She does homework every day.
This means that every day she does at least some homework.
It neither says nor implies that she completes her homework (because it doesn't specify what homework it's talking about).
It's also perfectly consistent with her doing other people's homework.
(For example, she might be a nanny who, among other tasks, helps with homework every day.)
She does her homework every day.
This means she does the homework that has been assigned to her, as opposed to doing other people's homework or helping others with their homework.
It also strongly implies that she completes her assignments, and doesn't just work on them for a bit.
(Because "does" implies completing and "her homework
" implies all of her homework.)
She does the homework every day.
This means there's some homework that both the speaker and listener are referring to, and she does that particular homework.
For example, "Mary is assigned math homework regularly.
She does the homework every day."
Which would mean she does that math homework.
It would be confusing to use this when the listener would not know what homework you are talking about.
ell.stackexchange.com/users/789/David Schwartz
They are all correct but can create slightly different implications.
Some examples:
She does homework every day, can't the teacher give them a break?
She does her homework
every day, she's such a great student.
She does the homework every day while her sister writes the book reports.
ell.stackexchange.com/users/5824/Johns-305
Both sentences are correct, I personally like more the first one "She does homework everyday" - the shorter the better.
Nonetheless if what you are looking for is to be more precise, the second one would be more detailed but in any case both are clear.
ell.stackexchange.com/users/40289/Cristian
Can I use the first example?    She does homework every day  She does her homework every day  She does the homework every day    Or is the object  her  required?
She does homework every day vs She does her homework every day vs She does the homework every day
ell.stackexchange.com
<articles><determiners><objects>
ell.stackexchange.com/questions/101308
ell.stackexchange.com/users/28147/masterkomp
They are all correct but can create slightly different implications.  You could certainly say that "her" is not required, as the reader is unlikely to suppose that she does someone else's homework.  It's not required for grammatical correctness, but in practice the version with the pronoun has a connotation of  all  of the subject's homework, while the version without is more indefinite.   All sentences are grammatically correct, but can have slightly different implications. "Her" is not required, but in practice it helps make the sentence more definitive.
All sentences are grammatically correct, but can have slightly different implications. "Her" is not required, but in practice it helps make the sentence more definitive.