poopey
Answered

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 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.