Question

Identify the degree of the terms and the degree of the polynomial.

4a⁴ b-9a⁶ +4b⁸ -5
a) Term degrees: (4, 6, 8, 0); Polynomial degree: 8
b) Term degrees: (4, 6, 8, -5); Polynomial degree: 4
c) Term degrees: (4, -9, 4, -5); Polynomial degree: 6
d) Term degrees: (4, 6, 8, -5); Polynomial degree: 8

Answer 1

The term degrees for the polynomial 4a⁴b - 9a⁶ + 4b⁸ - 5 are (5, 6, 8, 0), as we sum the exponents of the variables in each term to get the term degrees. The degree of the polynomial is 8, as it is the highest term degree.

Step-by-step explanation:

The question asks us to identify the degree of the terms and the degree of the polynomial for the expression 4a⁴b - 9a⁶ + 4b⁸ - 5. The degree of a term in a polynomial is the sum of the exponents of the variables in the term. To find the degrees of the given terms, we examine each term separately:

• The first term, 4a⁴b, has a degree of 4 (from a⁴) + 1 (from b), which gives us 5.
• The second term, -9a⁶, has a degree of 6.
• The third term, 4b⁸, has a degree of 8.
• The fourth term, -5, is a constant with no variables, so its degree is 0.

Therefore, the term degrees are (5, 6, 8, 0). The degree of the polynomial is the highest degree of any term in the polynomial, which in this case is 8. So the correct answer is: Term degrees: (5, 6, 8, 0); Polynomial degree: 8