Which polynomial is in standard form?

A. [tex]1 + 2x - 8x^2 + 6x^3[/tex]

B. [tex]2x^2 + 6x^3 - 9x + 12[/tex]

C. [tex]6x^3 + 5x - 3x^2 + 2[/tex]

D. [tex]2x^3 + 4x^2 - 7x + 5[/tex]



Answer :

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.