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Answer :
To determine the standard form of a polynomial, we need to arrange the terms in descending order based on their degree, with the highest power first.
Let's consider the polynomial terms given:
1. [tex]\( 9x^2 + 5x + 27 + 2x^3 \)[/tex]
2. [tex]\( 2x^3 + 9x^2 + 5x + 27 \)[/tex]
3. [tex]\( 27 + 5x + 9x^2 + 2x^3 \)[/tex]
### Steps to Find the Standard Form
1. Identify the Degrees of Terms:
- The degree of a term is the power of [tex]\( x \)[/tex] in that term.
- [tex]\( 2x^3 \)[/tex] has a degree of 3.
- [tex]\( 9x^2 \)[/tex] has a degree of 2.
- [tex]\( 5x \)[/tex] has a degree of 1.
- [tex]\( 27 \)[/tex] is a constant term with a degree of 0.
2. Order the Terms by Degree:
- The standard form arranges terms from the highest degree to the lowest degree.
3. Arrange the Given Terms:
- Start with the term with the highest degree, followed by the next highest, and so on.
Following these steps, let's compare the given options:
- Option 1: [tex]\( 9x^2 + 5x + 27 + 2x^3 \)[/tex]
- Rearranged, it's [tex]\( 2x^3 + 9x^2 + 5x + 27 \)[/tex].
- Option 2: [tex]\( 2x^3 + 9x^2 + 5x + 27 \)[/tex]
- This is already in descending order of degree.
- Option 3: [tex]\( 27 + 5x + 9x^2 + 2x^3 \)[/tex]
- Rearranged, it's [tex]\( 2x^3 + 9x^2 + 5x + 27 \)[/tex].
Thus, the terms in Option 2 are already correctly ordered in standard form, which is:
[tex]\[ 2x^3 + 9x^2 + 5x + 27 \][/tex]
This is the standard form of the polynomial.
Let's consider the polynomial terms given:
1. [tex]\( 9x^2 + 5x + 27 + 2x^3 \)[/tex]
2. [tex]\( 2x^3 + 9x^2 + 5x + 27 \)[/tex]
3. [tex]\( 27 + 5x + 9x^2 + 2x^3 \)[/tex]
### Steps to Find the Standard Form
1. Identify the Degrees of Terms:
- The degree of a term is the power of [tex]\( x \)[/tex] in that term.
- [tex]\( 2x^3 \)[/tex] has a degree of 3.
- [tex]\( 9x^2 \)[/tex] has a degree of 2.
- [tex]\( 5x \)[/tex] has a degree of 1.
- [tex]\( 27 \)[/tex] is a constant term with a degree of 0.
2. Order the Terms by Degree:
- The standard form arranges terms from the highest degree to the lowest degree.
3. Arrange the Given Terms:
- Start with the term with the highest degree, followed by the next highest, and so on.
Following these steps, let's compare the given options:
- Option 1: [tex]\( 9x^2 + 5x + 27 + 2x^3 \)[/tex]
- Rearranged, it's [tex]\( 2x^3 + 9x^2 + 5x + 27 \)[/tex].
- Option 2: [tex]\( 2x^3 + 9x^2 + 5x + 27 \)[/tex]
- This is already in descending order of degree.
- Option 3: [tex]\( 27 + 5x + 9x^2 + 2x^3 \)[/tex]
- Rearranged, it's [tex]\( 2x^3 + 9x^2 + 5x + 27 \)[/tex].
Thus, the terms in Option 2 are already correctly ordered in standard form, which is:
[tex]\[ 2x^3 + 9x^2 + 5x + 27 \][/tex]
This is the standard form of the polynomial.
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