Let's break down the task into steps:

1. Number of Terms: This refers to how many distinct parts (terms) are separated by plus or minus signs in a polynomial.

2. Degree: The degree of a polynomial is determined by the highest exponent of the variable in any of the terms.

3. Naming: Polynomials can be classified based on the number of terms and their degree:

   • Number of terms:
     • 1 term: Monomial
     • 2 terms: Binomial
     • 3 terms: Trinomial
     • 4 or more terms: Polynomial (though all are technically polynomials)
   • Degree:
     • Degree 0: Constant (no variable present)
     • Degree 1: Linear (highest exponent is 1)
     • Degree 2: Quadratic (highest exponent is 2)
     • Degree 3: Cubic (highest exponent is 3)
     • Degree 4: Quartic (highest exponent is 4)
     • Degree 5: Quintic (highest exponent is 5)

Example:

Consider the polynomial:
$4x^3 + 5x^2 - 2x + 7$

• Number of terms: 4 (since there are four separate parts: $4x^3$, $5x^2$, $-2x$, and $7$)
• Degree: 3 (the highest exponent is 3, in the term $4x^3$)
• Name: Since it has four terms and the highest degree is 3, this is a cubic polynomial with 4 terms.

To complete your specific question:

• Identify each polynomial (if given in activity 1).
• Count the terms.
• Find the degree.
• Name each polynomial based on its terms and degree.

Would you like to provide specific polynomials, or should I illustrate more examples?

Follow-up Questions:

1. Can you list the polynomials you are referring to?
2. What is the most complex polynomial degree in the box of activity 1?
3. Do you need an explanation of how to calculate the degree of multivariable polynomials?
4. Is there any uncertainty regarding classifying by the number of terms?
5. Are there any questions about how polynomials are added or multiplied?

Tip:

To identify the degree of a polynomial, always check the highest power of any variable, even if it appears in the middle of the polynomial.