Answer :
A polynomial is in standard form when its terms are arranged in descending order by their degree (the exponent on [tex]\( x \)[/tex]). Let's analyze each option:
1. The polynomial is
[tex]$$2x^4 + 6 + 24x^5.$$[/tex]
If we rearrange it in descending order by the exponents, it becomes
[tex]$$24x^5 + 2x^4 + 6.$$[/tex]
Since the given expression is not written in that order, it is not in standard form.
2. The polynomial is
[tex]$$6x^2 - 9x^3 + 12x^4.$$[/tex]
Rearranging the terms in descending order gives
[tex]$$12x^4 - 9x^3 + 6x^2.$$[/tex]
Again, the given expression is not in descending order and thus is not in standard form.
3. The polynomial is
[tex]$$19x + 6x^2 + 2.$$[/tex]
In descending order, it should be written as
[tex]$$6x^2 + 19x + 2.$$[/tex]
Since it is not arranged this way in the given version, it is not in standard form.
4. The polynomial is
[tex]$$23x^9 - 12x^4 + 19.$$[/tex]
Here, the terms already appear in descending order of the exponents (i.e., [tex]\(9\)[/tex], [tex]\(4\)[/tex], and [tex]\(0\)[/tex] respectively).
Since option 4 is already written with the terms in descending order of degree, it is the polynomial in standard form.
Thus, the answer is option 4.
1. The polynomial is
[tex]$$2x^4 + 6 + 24x^5.$$[/tex]
If we rearrange it in descending order by the exponents, it becomes
[tex]$$24x^5 + 2x^4 + 6.$$[/tex]
Since the given expression is not written in that order, it is not in standard form.
2. The polynomial is
[tex]$$6x^2 - 9x^3 + 12x^4.$$[/tex]
Rearranging the terms in descending order gives
[tex]$$12x^4 - 9x^3 + 6x^2.$$[/tex]
Again, the given expression is not in descending order and thus is not in standard form.
3. The polynomial is
[tex]$$19x + 6x^2 + 2.$$[/tex]
In descending order, it should be written as
[tex]$$6x^2 + 19x + 2.$$[/tex]
Since it is not arranged this way in the given version, it is not in standard form.
4. The polynomial is
[tex]$$23x^9 - 12x^4 + 19.$$[/tex]
Here, the terms already appear in descending order of the exponents (i.e., [tex]\(9\)[/tex], [tex]\(4\)[/tex], and [tex]\(0\)[/tex] respectively).
Since option 4 is already written with the terms in descending order of degree, it is the polynomial in standard form.
Thus, the answer is option 4.
