Choose the polynomial written in standard form.

yes, the last one.

Assuming you know what the standard form is (highest degree first), then can you determine the degree of each term? Just add exponents of all the variables.

what if two terms have the same degree? I have checked a few discussions, and none mentions that wrinkle. Check your text or teacher. Usually I list the variables in order decreasing powers.

So, for these, I'd say only the last is in standard form. The first I'd write as

10x^9 + 4x^4y + x^3y^2
so that the last two terms, both of degree 5, have the x's in descending order.

Yes, the last polynomial, x^4y^5 + 4x^3y^2 + 10x^2, is written in standard form.

To determine whether the last polynomial, x^4y^5 + 4x^3y^2 + 10x^2, is written in standard form, we need to check if its terms are arranged in descending order of their exponents.

The polynomial has three terms:
1) x^4y^5
2) 4x^3y^2
3) 10x^2

Let's compare the exponents of the variables in each term. In the first term, x has an exponent of 4 and y has an exponent of 5. In the second term, x has an exponent of 3 and y has an exponent of 2. Finally, in the third term, there is no y variable, so as a convention, we can assign it an exponent of 0, and x has an exponent of 2.

Since it is required to arrange the terms in descending order of their exponents, we can rewrite the polynomial in standard form as:

x^4y^5 + 4x^3y^2 + 10x^2

Therefore, the last option you provided, x^4y^5 + 4x^3y^2 + 10x^2, is written in standard form.