Question

# Use the Rational Zero Theorem to list all possible rational zeros for the function f(x) = x^3 + x^2 - 4x - 4.

Rational functions
Use the Rational Zero Theorem to list all possible rational zeros for the function $$f(x) = x^3 + x^2 - 4x - 4$$.

2020-11-09

possible rational $$zeros=(Factors\ of\ the\ constant\ term)/(Factors\ of\ the\ leading\ coefficient)$$
List the factors of the constant term and the leading coefficient of the given function.
Factors of the constant term, -4: +-1, +-2, +-4
Factors of leading co efficient, 1: +-1
possible rational $$zeros=(Factors\ of\ -4)/(Factors\ of\ 1)$$
$$=(+-1,+-2,+-4)/(+-1)$$
consider each number is numerator an divide it by each number in the denominator.
Possible rational zeros= +-1, +-2, +-4
Therefore, the possible rational seros of f(x) are
+-1, +-2 and +-4