Which polynomials are in standard form?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)   
\[t^4-1\]
A
\[t^4-1\]
(Choice B)   
\[-2t^2+3t+4\]
B
\[-2t^2+3t+4\]
(Choice C)   
\[4t-7\]
C
\[4t-7\]
(Choice D)   None of the above
D
None of the above

Polynomials in standard form are written with terms in descending order of their exponents. Let's analyze each choice:

- **Choice A**: \( t^4 - 1 \)
  - This is in standard form because the terms are arranged in descending order of their exponents (4, then 0).

- **Choice B**: \(-2t^2 + 3t + 4\)
  - This is also in standard form. The terms are arranged in descending order of their exponents (2, 1, then 0).

- **Choice C**: \( 4t - 7 \)
  - This is in standard form as well. The terms are arranged in descending order of their exponents (1, then 0).

Given these analyses, the correct answers are:

- (A) \( t^4 - 1 \)
- (B) \(-2t^2 + 3t + 4\)
- (C) \( 4t - 7 \)

**Would you like more details or have any questions about polynomial standard forms?**

Here are 8 related questions for further exploration:

1. What defines a polynomial in standard form?
2. Can a polynomial have fractional exponents and still be in standard form?
3. How would you convert \(3 + 2t^3 - 5t^2\) to standard form?
4. Are all polynomials with the same terms but different orders equivalent?
5. How does the standard form help in polynomial operations like addition and multiplication?
6. What is the degree of a polynomial and how is it determined?
7. How can you factorize a polynomial in standard form?
8. What are the implications of a polynomial not being in standard form for calculus operations?

**Tip**: When writing polynomials, always arrange the terms in descending order of the exponents to ensure it is in standard form.

Explore examples and explanations of polynomials in standard form. Learn how to identify polynomials like t^4 - 1, -2t^2 + 3t + 4, and 4t - 7, arranged in descending order of their exponents. Suitable for students in Grades 7-9.

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