Question

the possible rational roots of
\\y^4 - y^3 - 3y^2 - y + 15\\
are \\(y = \\) input box (list all possible roots, separated by commas. enter positive and negative roots separately)

Explanation:

Step1: Identify coefficients

Identify the leading coefficient \(a_n = 1\) and the constant term \(a_0 = 15\).

Step2: Find factors of constant

Find all integer factors of the constant term \(15\).

$$p \in \{\pm 1, \pm 3, \pm 5, \pm 15\}$$

Step3: Find factors of leading coefficient

Find all integer factors of the leading coefficient \(1\).

$$q \in \{\pm 1\}$$

Step4: List possible rational roots

Form all possible fractions \(\frac{p}{q}\) to get the roots.

$$y \in \{1, -1, 3, -3, 5, -5, 15, -15\}$$

Answer:

\(1, -1, 3, -3, 5, -5, 15, -15\)