Question: What are the degree and leading coefficient of the polynomial? \[ -8x + 12x^3 + 5x^2 - 6 \]…

What are the degree and leading coefficient of the polynomial?

\[ -8x + 12x^3 + 5x^2 - 6 \]

Degree: \(\boxed{\quad}\)

Leading coefficient: \(\boxed{\quad}\)

Solution

To find the degree and leading coefficient of the polynomial: The polynomial given is \[ -8x + 12x^3 + 5x^2 - 6 \] First, identify the term with the highest exponent, as this determines the degree of the polynomial. The term with the highest exponent is \(12x^3\). Thus, the degree of the polynomial is 3. The leading coefficient is the coefficient of the term with the highest degree. In this case, the leading coefficient is 12. Therefore, the degree is 3, and the leading coefficient is 12.