To determine which statement best describes the polynomial [tex]\(13y^8 - 4y^7 + 3y\)[/tex], let's explore what each statement means in the context of polynomial characteristics.
### 1. The coefficients are in order from highest to lowest.
This statement suggests that the polynomial is arranged by the coefficients decreasing numerically. However, polynomial standard form is not determined by the order of coefficients but rather by the exponents.
### 2. The exponents are in order from highest to lowest.
In standard form, a polynomial must be arranged such that the terms are ordered by descending powers of the variable. That means for the polynomial [tex]\(13y^8 - 4y^7 + 3y\)[/tex], the highest power of [tex]\( y \)[/tex], which is [tex]\( y^8 \)[/tex], appears first, followed by [tex]\( y^7 \)[/tex], and then [tex]\( y \)[/tex]. In this case, the given polynomial follows this convention as the exponents [tex]\(8, 7,\)[/tex] and [tex]\(1\)[/tex] are in descending order.
### 3. There is no constant.
A polynomial does not need to lack a constant term to be considered in standard form. The standard form is about the order of exponents, not the presence or absence of constants.
### 4. The coefficients cannot be further simplified.
This statement is irrelevant to defining whether a polynomial is in standard form. Simplification of coefficients relates to their numerical reduction, not the arrangement of terms in standard form.
### Conclusion
The best description of the polynomial [tex]\(13y^8 - 4y^7 + 3y\)[/tex] is that it is in standard form because the exponents are in order from highest to lowest. This correctly captures the essence of the standard polynomial form.
The correct answer is:
It is in standard form because the exponents are in order from highest to lowest.
