Answer :
A polynomial in standard form is written with its terms arranged in descending order of their degrees. Let's analyze each option:
1. For the polynomial
[tex]$$2x^4 + 6 + 24x^5,$$[/tex]
the degrees of the terms are [tex]$4$[/tex], [tex]$0$[/tex], and [tex]$5$[/tex]. Since the correct descending order should be [tex]$5$[/tex], [tex]$4$[/tex], [tex]$0$[/tex], the terms are not arranged correctly.
2. For the polynomial
[tex]$$6x^2 - 9x^3 + 12x^4,$$[/tex]
the degrees are [tex]$2$[/tex], [tex]$3$[/tex], and [tex]$4$[/tex]. The proper descending order is [tex]$4$[/tex], [tex]$3$[/tex], [tex]$2$[/tex], so this option is also not in standard form.
3. For the polynomial
[tex]$$19x + 6x^2 + 2,$$[/tex]
the degrees of the terms are [tex]$1$[/tex], [tex]$2$[/tex], and [tex]$0$[/tex]. The descending order should be [tex]$2$[/tex], [tex]$1$[/tex], [tex]$0$[/tex], hence this option is not in standard form.
4. For the polynomial
[tex]$$23x^9 - 12x^4 + 19,$$[/tex]
the degrees are [tex]$9$[/tex], [tex]$4$[/tex], and [tex]$0$[/tex], which is already in descending order.
Thus, the only polynomial that is in standard form is
[tex]$$23x^9 - 12x^4 + 19.$$[/tex]
1. For the polynomial
[tex]$$2x^4 + 6 + 24x^5,$$[/tex]
the degrees of the terms are [tex]$4$[/tex], [tex]$0$[/tex], and [tex]$5$[/tex]. Since the correct descending order should be [tex]$5$[/tex], [tex]$4$[/tex], [tex]$0$[/tex], the terms are not arranged correctly.
2. For the polynomial
[tex]$$6x^2 - 9x^3 + 12x^4,$$[/tex]
the degrees are [tex]$2$[/tex], [tex]$3$[/tex], and [tex]$4$[/tex]. The proper descending order is [tex]$4$[/tex], [tex]$3$[/tex], [tex]$2$[/tex], so this option is also not in standard form.
3. For the polynomial
[tex]$$19x + 6x^2 + 2,$$[/tex]
the degrees of the terms are [tex]$1$[/tex], [tex]$2$[/tex], and [tex]$0$[/tex]. The descending order should be [tex]$2$[/tex], [tex]$1$[/tex], [tex]$0$[/tex], hence this option is not in standard form.
4. For the polynomial
[tex]$$23x^9 - 12x^4 + 19,$$[/tex]
the degrees are [tex]$9$[/tex], [tex]$4$[/tex], and [tex]$0$[/tex], which is already in descending order.
Thus, the only polynomial that is in standard form is
[tex]$$23x^9 - 12x^4 + 19.$$[/tex]
