Answer:
Therefore, the potential roots of the function p(x) are ±6, ±1, and ±3. Options (1), (2), and (3) are true.
Explanation:
According to the Rational Root Theorem, the potential roots of a polynomial function are the rational numbers that can be obtained by dividing the factors of the constant term by the factors of the leading coefficient.
Let's analyze the provided options:
±6:
Constant term factors: ±1, ±2, ±3, ±4, ±6, ±12
Leading coefficient factor: ±1
Potential root: ±6 (dividing constant term factor by leading coefficient factor)
±1:
Constant term factors: ±1, ±2, ±3, ±4, ±6, ±12
Leading coefficient factor: ±1
Potential root: ±1 (dividing constant term factor by leading coefficient factor)
±3:
Constant term factors: ±1, ±2, ±3, ±4, ±6, ±12
Leading coefficient factor: ±1
Potential root: ±3 (dividing constant term factor by leading coefficient factor)
±8:
Not a factor of the constant term (12)
Not a potential root
Therefore, Options (1), (2), and (3) are true.