Question

answer the questions about the following polynomial.
$-4x^5 - x^4 - 7 - \frac{1}{4}x$
answer attempt 1 out of 3
the expression represents a dropdown polynomial with blank terms. the constant term is blank, thdropdown is blank, and the leading coefficient is blank.
dropdown options: quintic, quartic, linear, quadratic, cubic

Explanation:

Step1: Determine the degree of the polynomial

The polynomial is \(-4x^{5}-x^{4}-7-\frac{1}{4}x\). The degree of a polynomial is the highest power of \(x\) in it. Here, the highest power is \(5\) (from the term \(-4x^{5}\)). A polynomial with degree \(5\) is called a quintic polynomial.

Step2: Count the number of terms

The terms of the polynomial are \(-4x^{5}\), \(-x^{4}\), \(-7\), and \(-\frac{1}{4}x\). So there are \(4\) terms.

Step3: Identify the constant term

The constant term is the term without \(x\), which is \(-7\).

Step4: Find the leading term

The leading term is the term with the highest degree, which is \(-4x^{5}\).

Step5: Determine the leading coefficient

The leading coefficient is the coefficient of the leading term. For \(-4x^{5}\), the coefficient is \(-4\).

Answer:

The expression represents a quintic polynomial with \(4\) terms. The constant term is \(-7\), the leading term is \(-4x^{5}\), and the leading coefficient is \(-4\).