Answer :
To determine which polynomial is in standard form, we need to arrange the terms of each polynomial from highest degree to lowest degree of the variable [tex]\( x \)[/tex]. Let’s go through each option:
1. [tex]\( 2x^4 + 6 + 24x^5 \)[/tex]
- Rearrange by decreasing powers of [tex]\( x \)[/tex]:
- Standard form: [tex]\( 24x^5 + 2x^4 + 6 \)[/tex]
2. [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex]
- Rearrange by decreasing powers of [tex]\( x \)[/tex]:
- Standard form: [tex]\( 12x^4 - 9x^3 + 6x^2 \)[/tex]
3. [tex]\( 19x + 6x^2 + 2 \)[/tex]
- Rearrange by decreasing powers of [tex]\( x \)[/tex]:
- Standard form: [tex]\( 6x^2 + 19x + 2 \)[/tex]
4. [tex]\( 23x^9 - 12x^4 + 19 \)[/tex]
- This is already arranged in standard form, as the terms are ordered from the highest degree, [tex]\( x^9 \)[/tex], to the lowest, which is the constant term.
Thus, the polynomial that is already in standard form is [tex]\( 23x^9 - 12x^4 + 19 \)[/tex].
1. [tex]\( 2x^4 + 6 + 24x^5 \)[/tex]
- Rearrange by decreasing powers of [tex]\( x \)[/tex]:
- Standard form: [tex]\( 24x^5 + 2x^4 + 6 \)[/tex]
2. [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex]
- Rearrange by decreasing powers of [tex]\( x \)[/tex]:
- Standard form: [tex]\( 12x^4 - 9x^3 + 6x^2 \)[/tex]
3. [tex]\( 19x + 6x^2 + 2 \)[/tex]
- Rearrange by decreasing powers of [tex]\( x \)[/tex]:
- Standard form: [tex]\( 6x^2 + 19x + 2 \)[/tex]
4. [tex]\( 23x^9 - 12x^4 + 19 \)[/tex]
- This is already arranged in standard form, as the terms are ordered from the highest degree, [tex]\( x^9 \)[/tex], to the lowest, which is the constant term.
Thus, the polynomial that is already in standard form is [tex]\( 23x^9 - 12x^4 + 19 \)[/tex].
