Answered

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Which polynomial is in standard form?

A. [tex]\(2x^4 + 6 + 24x^5\)[/tex]
B. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
C. [tex]\(19x + 6x^2 + 2\)[/tex]
D. [tex]\(23x^9 - 12x^4 + 19\)[/tex]

Sagot :

GinnyAnswer
To determine which polynomial is already in standard form, we must verify that the polynomial's terms are ordered by descending powers of [tex]\(x\)[/tex]. Let's inspect each polynomial one by one:

1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- Rearrange the terms in descending order: [tex]\(24x^5 + 2x^4 + 6\)[/tex]

2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Rearrange the terms in descending order: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex]

3. [tex]\(19x + 6x^2 + 2\)[/tex]
- Rearrange the terms in descending order: [tex]\(6x^2 + 19x + 2\)[/tex]

4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial is already in descending order: [tex]\(23x^9 - 12x^4 + 19\)[/tex]

The fourth polynomial, [tex]\(23x^9 - 12x^4 + 19\)[/tex], is already in standard form because its terms are ordered by descending powers of [tex]\(x\)[/tex].

Thus, the polynomial that is in standard form is the fourth one, and it corresponds to the answer index 3.
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