Question

consider the following polynomial.
$s(x) = 4x^2(x + 5)(x - 8)$
step 1 of 2: find the degree and leading coefficient of $s(x)$.
answer how to enter your answer (opens in new window)
4 points
degree:
leading coefficient:

Explanation:

Step1: Expand the polynomial terms

To find the degree and leading coefficient, we first expand the polynomial. The polynomial is \( s(x) = 4x^2(x + 5)(x - 8) \). First, multiply the binomials \((x + 5)(x - 8)\):

$$
LATEXBLOCK0
$$

Then multiply by \(4x^2\):

$$
LATEXBLOCK1
$$

Step2: Identify degree and leading coefficient

The degree of a polynomial is the highest power of \(x\) in the polynomial. In \(4x^4-12x^3 - 160x^2\), the highest power of \(x\) is \(4\), so the degree is \(4\). The leading coefficient is the coefficient of the term with the highest degree. The term with the highest degree is \(4x^4\), so the leading coefficient is \(4\).

Answer:

Degree: \(4\)
Leading Coefficient: \(4\)