Final Answer:
The degree, leading coefficient, and constant values for the given polynomials are as follows:
- For f(x) = x³ - 8x² - x + 8, the degree is 3, the leading coefficient is 1, and the constant value is 8.
- For h(x) = 2x⁴ + x³ - 3x - 1, the degree is 4, the leading coefficient is 2, and the constant value is -1.
- For g(x) = 13.2r³ + 3r - x - 4, the degree is not explicitly stated, but it is the highest power of the variable (r), the leading coefficient is 13.2, and the constant value is -4.
Step-by-step explanation:
The degree of a polynomial is the highest power of the variable present in the expression. For f(x), the highest power is x³, so the degree is 3. Similarly, for h(x), the highest power is x⁴, so the degree is 4. In g(x), the degree is determined by the highest power of (r), which is r³ .
The leading coefficient is the coefficient of the term with the highest power. For f(x), the leading coefficient is 1, for h(x) it is 2, and for g(x) it is 13.2.
The constant value is the term without any variable. For f(x), the constant is 8, for h(x) it is -1, and for g(x) it is -4.
In conclusion, understanding the degree, leading coefficient, and constant values of polynomials provides insights into their behavior, including their complexity and the nature of their roots. These values play a crucial role in polynomial analysis and are fundamental in various mathematical applications.