To determine which polynomial is in standard form, we need to arrange each polynomial in descending order of the power of [tex]\(x\)[/tex].
Let's analyze each polynomial one by one:
1. For the polynomial [tex]\(1 + 2x - 8x^2 + 6x^3\)[/tex]:
- Rearrange the terms in descending order of [tex]\(x\)[/tex]:
[tex]\[
6x^3 - 8x^2 + 2x + 1
\][/tex]
2. For the polynomial [tex]\(2x^2 + 6x^3 - 9x + 12\)[/tex]:
- Rearrange the terms in descending order of [tex]\(x\)[/tex]:
[tex]\[
6x^3 + 2x^2 - 9x + 12
\][/tex]
3. For the polynomial [tex]\(6x^3 + 5x - 3x^2 + 2\)[/tex]:
- Rearrange the terms in descending order of [tex]\(x\)[/tex]:
[tex]\[
6x^3 - 3x^2 + 5x + 2
\][/tex]
4. For the polynomial [tex]\(2x^3 + 4x^2 - 7x + 5\)[/tex]:
- This polynomial is already in descending order of [tex]\(x\)[/tex]:
[tex]\[
2x^3 + 4x^2 - 7x + 5
\][/tex]
After arranging all the polynomials, we observe that the only polynomial that was already in standard form is:
[tex]\[ 2x^3 + 4x^2 - 7x + 5 \][/tex]
Therefore, the polynomial that is in standard form is the fourth polynomial:
[tex]\[ 2x^3 + 4x^2 - 7x + 5 \][/tex]
The correct answer is polynomial number 4.
