Question

what are the leading coefficient and degree of the polynomial?
$-6x^{2}-12x^{4}-4x^{5}+7x$
leading coefficient:
degree:

Explanation:

Step1: Arrange the polynomial in standard form

To find the leading coefficient and degree, we first write the polynomial in standard form (descending order of exponents). The given polynomial is \(-6x^{2}-12x^{4}-4x^{5}+7x\). When arranged in standard form, it becomes \(-4x^{5}-12x^{4}-6x^{2}+7x\).

Step2: Find the leading coefficient

The leading coefficient is the coefficient of the term with the highest degree. In the standard - form polynomial \(-4x^{5}-12x^{4}-6x^{2}+7x\), the term with the highest degree is \(-4x^{5}\), and the coefficient of this term is \(-4\). So, the leading coefficient is \(-4\).

Step3: Find the degree of the polynomial

The degree of a polynomial is the highest power (exponent) of the variable in the polynomial. In the polynomial \(-4x^{5}-12x^{4}-6x^{2}+7x\), the highest exponent of \(x\) is \(5\). So, the degree of the polynomial is \(5\).

Answer:

Leading coefficient: \(-4\)
Degree: \(5\)