Which statement best describes the polynomial?

[tex]\[ 13y^8 - 4y^7 + 3y \][/tex]

A. It is in standard form because the coefficients are in order from highest to lowest.
B. It is in standard form because the exponents are in order from highest to lowest.
C. It is in standard form because there is no constant.



Answer :

To determine which statement best describes the polynomial [tex]\( 13y^8 - 4y^7 + 3y \)[/tex], let's analyze its structure and properties step by step.

1. Identify Exponents and Coefficients:
- The given polynomial is [tex]\( 13y^8 - 4y^7 + 3y \)[/tex].
- The exponents of the terms are 8, 7, and 1.
- The coefficients of the terms are 13, -4, and 3.

2. Verify Presence of a Constant Term:
- A constant term in a polynomial is a term that does not contain any variables (like [tex]\( y \)[/tex] in this case).
- In the polynomial [tex]\( 13y^8 - 4y^7 + 3y \)[/tex], there is no term without [tex]\( y \)[/tex]. Hence, the polynomial has no constant term.

3. Determine the Order of Exponents:
- The polynomial terms are: [tex]\( 13y^8 \)[/tex], [tex]\( -4y^7 \)[/tex], and [tex]\( 3y \)[/tex].
- The exponents (8, 7, and 1) are arranged in descending order, from highest to lowest.

4. Evaluate if the Polynomial is in Standard Form:
- A polynomial is considered to be in standard form if its terms are arranged in descending order of the exponents.
- In this case, the polynomial [tex]\( 13y^8 - 4y^7 + 3y \)[/tex] does indeed have its terms arranged with exponents in descending order.

Given these analyses, the statement that best describes the polynomial is:

#### "It is in standard form because the exponents are in order from highest to lowest."