Question

consider the following polynomial.
$f(x) = x^2(x + 5)(x - 9)$
step 1 of 2: find the degree and leading coefficient of $f(x)$.
answerhow to enter your answer (opens in new window)
4 points
degree:
leading coefficient:

Explanation:

Step1: Expand the polynomial

To find the degree and leading coefficient, we first expand the polynomial \( f(x) = x^2(x + 5)(x - 9) \). First, multiply \( (x + 5)(x - 9) \):

$$
LATEXBLOCK0
$$

Then multiply by \( x^2 \):

$$
LATEXBLOCK1
$$

Step2: Identify degree and leading coefficient

The degree of a polynomial is the highest power of \( x \) in the polynomial. In \( f(x)=x^4 - 4x^3 - 45x^2 \), 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 \( x^4 \), and its coefficient is \( 1 \) (since \( x^4 = 1\cdot x^4 \)).

Answer:

Degree: \( 4 \)
Leading Coefficient: \( 1 \)