Question

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Answer 1

Answer: $\pm1,\pm3,\pm5, \pm15$

Step-by-step explanation:

We can list the possible rational roots of this polynomial using the Rational Root Theorem. This theorem states that all the possible rational roots of an equation follow the structure $\frac{p}{q}$, where p is any of the factors of the constant term and q is any of the factors of the leading coefficient.

In this example, -15 is the constant term and 1 is the leading coefficient ($x^4$ has a coefficient of 1).

The factors of -15 are $\pm1,\pm3,\pm5, \pm15$, while the factors of 1 are $\pm1$. p is can be any one of the factors of -15, while q can be any of the factors of 1.

$\frac{\pm1,\pm3,\pm5, \pm15}{\pm1}$

The possible roots can be any of the numbers on the top divided by any of the numbers on the bottom. Since dividing by 1 or -1 won't change any of the numbers on the top, the rational roots of this function are $\pm1,\pm3,\pm5, \pm15$.