To determine which polynomial is in standard form, we need to ensure that the terms are arranged in decreasing order of their exponents. Let’s go through each polynomial one by one:
1. [tex]\( 1 + 2x - 8x^2 + 6x^3 \)[/tex]:
Rearrange the terms in descending order of the exponents:
[tex]\[
6x^3 - 8x^2 + 2x + 1
\][/tex]
2. [tex]\( 2x^2 + 6x^3 - 9x + 12 \)[/tex]:
Rearrange the terms in descending order of the exponents:
[tex]\[
6x^3 + 2x^2 - 9x + 12
\][/tex]
3. [tex]\( 6x^3 + 5x - 3x^2 + 2 \)[/tex]:
Rearrange the terms in descending order of the exponents:
[tex]\[
6x^3 - 3x^2 + 5x + 2
\][/tex]
4. [tex]\( 2x^3 + 4x^2 - 7x + 5 \)[/tex]:
This polynomial is already in order:
[tex]\[
2x^3 + 4x^2 - 7x + 5
\][/tex]
The polynomial that is initially written in standard form (terms in decreasing order of their exponents) is the fourth one:
[tex]\[ 2x^3 + 4x^2 - 7x + 5 \][/tex]
Therefore, the polynomial that is in standard form is the fourth one in the given list.
