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."
