To determine which polynomials are in standard form, we first need to understand what it means for a polynomial to be in standard form. A polynomial is in standard form if its terms are ordered in descending powers of the variable. Let's analyze each polynomial given:
Option A: [tex]\(3z - 1\)[/tex]
- In this polynomial, the term [tex]\(3z\)[/tex] is of the first degree, and the constant term [tex]\(-1\)[/tex] is of zero degrees.
- The terms are already in descending order: [tex]\(z^1\)[/tex] followed by [tex]\(z^0\)[/tex].
- Therefore, this polynomial is in standard form.
Option B: [tex]\(2 + 4x - 5x^2\)[/tex]
- In this polynomial, the term [tex]\( -5x^2 \)[/tex] is of the second degree, [tex]\(4x\)[/tex] is of the first degree, and the constant term [tex]\(2\)[/tex] is of zero degrees.
- The terms are not ordered correctly in descending powers of [tex]\(x\)[/tex].
- To be in standard form, it should be rewritten as: [tex]\(-5x^2 + 4x + 2\)[/tex].
- Therefore, this polynomial is not in standard form.
Option C: [tex]\(-5p^5 + 2p^2 - 3p + 1\)[/tex]
- In this polynomial, [tex]\(-5p^5\)[/tex] is of the fifth degree, [tex]\(2p^2\)[/tex] is of the second degree, [tex]\(-3p\)[/tex] is of the first degree, and the constant term [tex]\(1\)[/tex] is of zero degrees.
- The terms are already in descending order of the powers of [tex]\(p\)[/tex].
- Therefore, this polynomial is in standard form.
So, the polynomials in standard form are:
- Option A: [tex]\(3z - 1\)[/tex]
- Option C: [tex]\(-5p^5 + 2p^2 - 3p + 1\)[/tex]
These correspond to answer:
- A. [tex]\(3z - 1\)[/tex]
- C. [tex]\(-5p^5 + 2p^2 - 3p + 1\)[/tex]
