Let's analyze the given polynomial expression:

$7x^5 - 8x^4 + 8x^2 - 4$

Question 1: How many terms are there?

A term is a part of the expression separated by addition or subtraction signs. The given expression has four terms:

1. $7x^5$
2. $-8x^4$
3. $8x^2$
4. $-4$

Thus, the answer is: 4 terms.

Question 2: What is the highest exponent?

The exponents in the given expression are 5, 4, and 2. The highest exponent is 5.

Thus, the answer is: 5.

Question 3: Is it in standard form? How do you know?

A polynomial is in standard form if the terms are written in descending order of exponents, from highest to lowest.

The given expression:
$7x^5 - 8x^4 + 8x^2 - 4$ is already written in descending order of exponents: 5, 4, 2, and the constant term (-4).

Thus, the answer is: Yes, it is in standard form because the terms are arranged from highest exponent to lowest exponent.

Would you like more clarification? Here are some related questions to explore:

1. What makes a polynomial different from other algebraic expressions?
2. How do you determine the degree of a polynomial?
3. Can polynomials have negative exponents?
4. How do you classify polynomials based on the number of terms?
5. How do you add or subtract polynomials?

Tip: The degree of a polynomial is the highest exponent in the expression. Always check the order of terms to ensure it's in standard form! 🚀