Let's go through the exercises from the image you uploaded.

Problem 7:

Write $5x^2 - 2 + 3x$ in standard form. Identify the leading coefficient.

• Standard form means ordering the terms from highest to lowest degree. So, the polynomial should be written as:
  $5x^2 + 3x - 2$
• The leading coefficient is the coefficient of the term with the highest degree. In this case, it is 5 (from $5x^2$).

Problem 8:

Write $8y + 7y^3$ in standard form.

• Rearrange terms from highest to lowest degree:
  $7y^3 + 8y$
• The leading coefficient is 7 (from $7y^3$).

Would you like to continue solving the rest of the questions, or do you have specific ones you need help with? Let me know if you'd like detailed steps for others as well.

Follow-up Questions:

1. How do you identify the degree of a polynomial?
2. What are the rules for adding or subtracting polynomials?
3. How do you factor polynomials in standard form?
4. What does it mean for polynomials to be in standard form?
5. How can you identify the constant term in a polynomial?

Tip: When writing polynomials in standard form, always ensure the exponents on variables are in descending order.