Question

Determine if the expression 7, y, minus, 6, y, squared, minus, y, to the power 7y−6y
2
−y
5
is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The given expression ______ a polynomial. The polynomial is a _____
and has a degree of ______.

Answer 1

To determine if the expression \( 7y - 6y^2 - y^7 \) is a polynomial, we need to evaluate the components of the expression:

1. A polynomial consists of variables raised to non-negative integer powers.
2. In the expression \( 7y - 6y^2 - y^7 \):
- \( 7y \) is a polynomial term (degree 1).
- \( -6y^2 \) is also a polynomial term (degree 2).
- \( -y^7 \) is a polynomial term (degree 7).

Since all terms are in the form \( ay^n \) where \( a \) is a coefficient and \( n \) is a non-negative integer, the expression meets the criteria for being a polynomial.

**Identifying the type and degree:**
- The highest degree among the terms is 7 from the term \( -y^7 \).
- Since it is a polynomial with multiple terms, it is classified as a **multinomial**.

Therefore, filling in the provided structure:

The given expression **is** a polynomial. The polynomial is a **multinomial** and has a degree of **7**.