Sure, let's solve these questions one by one:

1. Choose the correct classification of $5x + 2$.

   To classify $5x + 2$, we need to examine its degree and number of terms.

   • The highest exponent of $x$ is 1, so it is a first-degree polynomial.
   • It has two terms: $5x$ and 2, making it a binomial.

   Answer: First degree binomial

2. Choose the polynomial written in standard form.

   The standard form of a polynomial arranges the terms in descending order of the powers of $x$ (or the main variable).

   • $xy^2 + 4x^4y + 10x^2$
   • $x^4y^2 + 4x^3y + 10x$
   • $x^4y^2 + 4x^3y^5 + 10x^2$
   • $x^6y^2 + 4x^3y^8 + 10x$

   Here, the second option is the polynomial arranged in descending order of powers of $x$.

   Answer: $x^4y^2 + 4x^3y + 10x$

3. Choose the correct simplification of $(4x^3 - 3x - 7) + (3x^3 + 5x + 3)$.

   Combine like terms:

   • $4x^3 + 3x^3 = 7x^3$
   • $-3x + 5x = 2x$
   • $-7 + 3 = -4$

   Answer: $7x^3 + 2x - 4$

4. Choose the correct simplification of $(5x^2y^3z^4)(6x^3y^4z^2)$.

   Multiply the coefficients and add the exponents of like bases:

   • Coefficient: $5 \times 6 = 30$
   • $x^{2+3} = x^5$
   • $y^{3+4} = y^7$
   • $z^{4+2} = z^6$

   Answer: $30x^5y^7z^6$

5. Choose the correct simplification of $(5xy^7)^2(y^2)^3$.

   Simplify each part:

   • $(5xy^7)^2 = 25x^2y^{14}$
   • $(y^2)^3 = y^6$

   Combine the results:

   • $25x^2y^{14+6} = 25x^2y^{20}$

   Answer: $25x^2y^{20}$

Would you like more details or have any questions about these solutions?

Here are five additional questions you can ask:

1. How do you classify a polynomial based on its degree and terms?
2. What is the standard form of a polynomial?
3. How do you combine like terms in polynomial addition?
4. What are the rules for multiplying powers with the same base?
5. How do you simplify expressions with exponents?

Tip: When simplifying polynomials, always combine like terms by matching variables and their respective exponents.