Which polynomials are in standard form?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)   
\[3z-1\]
A
\[3z-1\]
(Choice B)   
\[2+4x-5x^2\]
B
\[2+4x-5x^2\]
(Choice C)   
\[-5p^5+2p^2-3p+1\]
C
\[-5p^5+2p^2-3p+1\]
(Choice D)   None of the above
D
None of the above

To determine which polynomials are in standard form, we need to check if each polynomial is written in descending order of the exponents of the variable. 

Let's analyze each option:

- **Choice A:** \(3z - 1\)  
  This polynomial is in standard form because the term with the highest degree, \(3z\) (which is \(z^1\)), comes first, followed by the constant term \(-1\).

- **Choice B:** \(2 + 4x - 5x^2\)  
  This polynomial is **not** in standard form. The correct standard form would be to write the terms in descending order of the exponents: \(-5x^2 + 4x + 2\).

- **Choice C:** \(-5p^5 + 2p^2 - 3p + 1\)  
  This polynomial is in standard form because the terms are already arranged in descending order of the exponents: \(5\), \(2\), \(1\), and \(0\).

- **Choice D:** None of the above  
  Since both Choice A and Choice C are in standard form, this option is incorrect.

### Correct Answers:
- **Choice A** \(3z - 1\)
- **Choice C** \(-5p^5 + 2p^2 - 3p + 1\)

Would you like more details or have any questions about polynomials?

### Relative Questions:
1. How do you rewrite a polynomial to put it in standard form?
2. What is the degree of the polynomial \(3z - 1\)?
3. Why is the polynomial \(2 + 4x - 5x^2\) not in standard form?
4. Can a constant be considered a polynomial? If yes, what is its degree?
5. What does it mean for a polynomial to be in "descending order"?
6. What is the leading coefficient of the polynomial \(-5p^5 + 2p^2 - 3p + 1\)?
7. How do you determine the degree of a polynomial?
8. Can a polynomial have a negative leading coefficient?

### Tip:
When writing polynomials in standard form, always arrange the terms from the highest exponent to the lowest exponent.

Understand how to identify polynomials in standard form with clear explanations and examples. Learn why certain polynomials like 2 + 4x - 5x^2 are not in standard form and how to rearrange them correctly. Suitable for students in Grades 7-9.

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