Answer:
The correct answer is given by option a.
Step-by-step explanation:
Rational roots theorem:
In the rational roots theorem, we take the leading coefficient(which multiplies the term of x with the highest exponent) and the independent term(which does not multiply any value of x).
The possible roots have the format p/q, in which p are the factors of the independent term, and q are the factors of the leading coefficient.
In this question:
Leading coefficient: 3
Independent term: 15
Factors of the independent term: {1, 3, 5, 15} -> p
Factors of the leading coefficient: {1,3} -> q
Possible roots:
All possible values, positive or negative, in which p is divided by q. So
[tex]\pm \frac{1}{1}, \pm \frac{1}{3}, \pm \frac{3}{1}, \pm \frac{3}{3}, \pm \frac{5}{1}, \pm \frac{5}{3}, \pm \frac{15}{1}, \pm \frac{15}{3}[/tex]
So, without the repeated terms, they are:
[tex]\pm \frac{1}{3}, \pm \frac{5}{3}, \pm 1, \pm 3, \pm 5, \pm 15[/tex]
The correct answer is given by option a.
