Question

the following equation is given. complete parts (a)-(c)
\\x^3 - 5x^2 - 4x + 20 = 0\\

a. list all rational roots that are possible according to the rational zero theorem.
(use a comma to separate answers as needed.)

Explanation:

Identify the coefficients of the polynomial

Using the Rational Root Theorem knowledge point

$$
LATEXBLOCK0
$$

Find factors of the constant term and leading coefficient

Using the Rational Root Theorem knowledge point

$$
LATEXBLOCK1
$$

List all possible rational roots

Using the Rational Root Theorem knowledge point

$$ \frac{p}{q} \in \{\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20\} $$

Answer:

a. List all rational roots that are possible according to the Rational Zero Theorem.

<blank>\(1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 20, -20\)</blank>

(Use a comma to separate answers as needed.)