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Identify the degree, leading coefficient, and constant value of each of the following polynomials:

a. [tex]f(x) = 8x^3 - 88x^2 - x^8[/tex]

b. [tex]h(x) = 2x^4 - 23x^3 - 3x^2 - x[/tex]

c. [tex]g(x) = 13x^4 - 3x^3 - 8x^2 - 44[/tex]

Answer :

Final answer:

The degree of a polynomial is the highest power of x in the polynomial, the leading coefficient is the coefficient of the term with highest power, and the constant value is the term that doesn't include x. For the given polynomials f(x), h(x), and g(x), their respective degrees, leading coefficients, and constants have been determined.

Explanation:

The given functions are polynomials. For each polynomial, the degree is the highest power of x, the leading coefficient is the number before this term, and the constant value is the term with no x.

For the polynomial f(x) = 8x³ - 88x² - x^8, the terms are not in descending order of power. If rearranged, it becomes -x^8 + 8x³ - 88x². Therefore, the degree is 8, the leading coefficient is -1, and the constant term is 0 (since none is given).

The polynomial h(x) = 2x^4 - 23x³ - 3² - x has a degree of 4, a leading coefficient of 2, and a constant term of 0.

Finally, the polynomial g(x) = 13x^4 - 3x³ - 8x² - 44 has a degree of 4, a leading coefficient of 13 and a constant term of -44.

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