Questions: Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial as constant, linear, quadratic, cubic, or quartic. g(x) = 8x^3 - 2/3 x + 6

Solution Steps

To determine the leading term, the leading coefficient, and the degree of the polynomial, we need to identify the term with the highest power of \( x \). The leading term is the term with the highest exponent, the leading coefficient is the coefficient of that term, and the degree is the exponent of that term. Finally, we classify the polynomial based on its degree.

The leading term of the polynomial \( g(x) = 8x^3 - \frac{2}{3}x + 6 \) is the term with the highest power of \( x \). In this case, the leading term is \( 8x^3 \).

The leading coefficient is the coefficient of the leading term. For the leading term \( 8x^3 \), the leading coefficient is \( 8 \).

The degree of the polynomial is the exponent of the leading term. Since the leading term is \( 8x^3 \), the degree of the polynomial is \( 3 \).

Based on the degree, we classify the polynomial. Since the degree is \( 3 \), the polynomial is classified as cubic.

Final Answer