Answer: Possible rational zeros are ±1, ±2, ±3, ±4, ±6, ±12
Explanation:
The given function is
f(x) = x^3 - 3x^2 - 4x + 12
The rational zero theorem states that
if p(x) is a polynomial with integer coefficients and if p/q is a zero of p(x) or p(p/q) = 0, then p is a factor of the constant term of p(x) and q is a factor of the leading coefficient of p(x). The leading coefficient is the coefficient of the term with the highest exponent. The steps for applying this theorem to the given polynomial as shown below
Factors of constant term or 12 = ±1, ±2, ±3, ±4, ±6, ±9
factors of leading coefficient or 1 = ±1
Possible values of p/q = ±1/1, ±2/1, ±3/1, ±4/1, ±6/1, ±12/1
