To determine which polynomials are in standard form, we need to ensure that the terms within each polynomial are arranged in descending order of the powers of the variable.
Let's analyze each polynomial individually:
### Polynomial A:
[tex]\[3z - 1\][/tex]
- The polynomial contains terms [tex]\(3z\)[/tex] and [tex]\(-1\)[/tex].
- The term [tex]\(3z\)[/tex] has a power of 1.[tex]\(z\)[/tex] and [tex]\(-1\)[/tex] has a power of 0.
- The terms are arranged in descending powers of [tex]\(z\)[/tex]: 1 and 0.
Thus, Polynomial A is in standard form.
### Polynomial B:
[tex]\[2 + 4x - 5x^2\][/tex]
- The polynomial contains terms [tex]\(2\)[/tex], [tex]\(4x\)[/tex], and [tex]\(-5x^2\)[/tex].
- The term [tex]\(-5x^2\)[/tex] has a power of 2, [tex]\(4x\)[/tex] has a power of 1, and [tex]\(2\)[/tex] has a power of 0.
- However, the terms are not arranged in descending powers of [tex]\(x\)[/tex]. The term with the highest power, [tex]\(-5x^2\)[/tex], should come first.
Thus, Polynomial B is not in standard form.
### Polynomial C:
[tex]\[-5p^5 + 2p^2 - 3p + 1\][/tex]
- The polynomial contains terms [tex]\(-5p^5\)[/tex], [tex]\(2p^2\)[/tex], [tex]\(-3p\)[/tex], and [tex]\(1\)[/tex].
- The term [tex]\(-5p^5\)[/tex] has a power of 5, [tex]\(2p^2\)[/tex] has a power of 2, [tex]\(-3p\)[/tex] has a power of 1, and [tex]\(1\)[/tex] has a power of 0.
- The terms are arranged in descending powers of [tex]\(p\)[/tex]: 5, 2, 1, and 0.
Thus, Polynomial C is in standard form.
### Polynomial D:
- This states "None of the above," but we have already determined that there are polynomials in standard form.
Based on our detailed analysis, Polynomials A and C are in standard form.
Therefore, the correct selections are:
[tex]\[ \boxed{A \text{ and } C} \][/tex]
