Answer :
To determine which polynomial is in standard form, let's first understand what "standard form" means for polynomials. A polynomial is in standard form when its terms are arranged in descending order of their exponents.
Let's check each of the provided polynomials:
1. [tex]\( 2x^4 + 6 + 24x^5 \)[/tex]
- The terms are [tex]\( 2x^4 \)[/tex], constant [tex]\( 6 \)[/tex], and [tex]\( 24x^5 \)[/tex].
- The correct order should be descending powers, so rearrange to [tex]\( 24x^5 + 2x^4 + 6 \)[/tex].
- This is not in standard form as given.
2. [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex]
- The terms are [tex]\( 6x^2 \)[/tex], [tex]\( -9x^3 \)[/tex], and [tex]\( 12x^4 \)[/tex].
- Rearrange to [tex]\( 12x^4 - 9x^3 + 6x^2 \)[/tex].
- This is not in standard form as given.
3. [tex]\( 19x + 6x^2 + 2 \)[/tex]
- The terms are [tex]\( 19x \)[/tex], [tex]\( 6x^2 \)[/tex], and constant [tex]\( 2 \)[/tex].
- Rearrange to [tex]\( 6x^2 + 19x + 2 \)[/tex].
- This is not in standard form as given.
4. [tex]\( 23x^9 - 12x^4 + 19 \)[/tex]
- The terms are [tex]\( 23x^9 \)[/tex], [tex]\( -12x^4 \)[/tex], and constant [tex]\( 19 \)[/tex].
- These terms are in descending order of their exponents: [tex]\( 9, 4, \)[/tex] and then constant.
- This is in standard form.
After analyzing each polynomial, we conclude that:
The polynomial [tex]\( 23x^9 - 12x^4 + 19 \)[/tex] is in standard form.
Let's check each of the provided polynomials:
1. [tex]\( 2x^4 + 6 + 24x^5 \)[/tex]
- The terms are [tex]\( 2x^4 \)[/tex], constant [tex]\( 6 \)[/tex], and [tex]\( 24x^5 \)[/tex].
- The correct order should be descending powers, so rearrange to [tex]\( 24x^5 + 2x^4 + 6 \)[/tex].
- This is not in standard form as given.
2. [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex]
- The terms are [tex]\( 6x^2 \)[/tex], [tex]\( -9x^3 \)[/tex], and [tex]\( 12x^4 \)[/tex].
- Rearrange to [tex]\( 12x^4 - 9x^3 + 6x^2 \)[/tex].
- This is not in standard form as given.
3. [tex]\( 19x + 6x^2 + 2 \)[/tex]
- The terms are [tex]\( 19x \)[/tex], [tex]\( 6x^2 \)[/tex], and constant [tex]\( 2 \)[/tex].
- Rearrange to [tex]\( 6x^2 + 19x + 2 \)[/tex].
- This is not in standard form as given.
4. [tex]\( 23x^9 - 12x^4 + 19 \)[/tex]
- The terms are [tex]\( 23x^9 \)[/tex], [tex]\( -12x^4 \)[/tex], and constant [tex]\( 19 \)[/tex].
- These terms are in descending order of their exponents: [tex]\( 9, 4, \)[/tex] and then constant.
- This is in standard form.
After analyzing each polynomial, we conclude that:
The polynomial [tex]\( 23x^9 - 12x^4 + 19 \)[/tex] is in standard form.
