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Answer :
To determine which polynomial is written in standard form, we need to understand what standard form is. A polynomial is in standard form when its terms are ordered from highest to lowest degree based on the powers of [tex]\( x \)[/tex].
Let's look at each option:
1. [tex]\( 11 - 3x + 8x^2 + 9x^3 \)[/tex]: This polynomial is not in standard form because the terms are not ordered from highest to lowest degree. The term with [tex]\( x^3 \)[/tex] should come first.
2. [tex]\( -3x + 8x^2 + 9x^3 - 11 \)[/tex]: This polynomial is also not in standard form. The correct order would begin with the term containing [tex]\( x^3 \)[/tex].
3. [tex]\( 8x^2 + 9x^3 - 11 - 3x \)[/tex]: Again, this one is not in standard form. The terms should start with the one containing [tex]\( x^3 \)[/tex].
4. [tex]\( 9x^3 + 8x^2 - 3x - 11 \)[/tex]: This polynomial is indeed in standard form because the terms are ordered from the highest degree (degree 3) to the lowest (degree 0).
Therefore, the polynomial [tex]\( 9x^3 + 8x^2 - 3x - 11 \)[/tex] is the one written in standard form.
Let's look at each option:
1. [tex]\( 11 - 3x + 8x^2 + 9x^3 \)[/tex]: This polynomial is not in standard form because the terms are not ordered from highest to lowest degree. The term with [tex]\( x^3 \)[/tex] should come first.
2. [tex]\( -3x + 8x^2 + 9x^3 - 11 \)[/tex]: This polynomial is also not in standard form. The correct order would begin with the term containing [tex]\( x^3 \)[/tex].
3. [tex]\( 8x^2 + 9x^3 - 11 - 3x \)[/tex]: Again, this one is not in standard form. The terms should start with the one containing [tex]\( x^3 \)[/tex].
4. [tex]\( 9x^3 + 8x^2 - 3x - 11 \)[/tex]: This polynomial is indeed in standard form because the terms are ordered from the highest degree (degree 3) to the lowest (degree 0).
Therefore, the polynomial [tex]\( 9x^3 + 8x^2 - 3x - 11 \)[/tex] is the one written in standard form.
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