Question

what are the degree and leading coefficient of the polynomial? -20v³ + 18 + 12v² degree: leading coefficient:

Explanation:

Step1: Rearrange the polynomial

First, we rearrange the polynomial in standard form (descending order of exponents). The given polynomial is \(-20v^{3}+18 + 12v^{2}\), and when rearranged, it becomes \(-20v^{3}+12v^{2}+18\).

Step2: Find the degree

The degree of a polynomial is the highest power (exponent) of the variable. In the polynomial \(-20v^{3}+12v^{2}+18\), the exponents of \(v\) are \(3\), \(2\), and \(0\) (for the constant term \(18 = 18v^{0}\)). The highest exponent is \(3\), so the degree of the polynomial is \(3\).

Step3: Find the leading coefficient

The leading coefficient is the coefficient of the term with the highest degree (the leading term). The leading term in \(-20v^{3}+12v^{2}+18\) is \(-20v^{3}\), and the coefficient of this term is \(-20\). So the leading coefficient is \(-20\).

Answer:

Degree: \(3\)
Leading coefficient: \(-20\)