Question

Use the Rational Zero Theorem to list all possible rational zeros for the given function f(x) = x + 20x² - 16x - 14.

a) -1, -14
b) -1, -2, -7, -14
c) -2, -7, -14
d) -1, -2, -7, -14, 14

Answer 1

The possible rational zeros are the factors of the constant term ±(1, 2, 7, 14), because the leading coefficient is 1.

Step-by-step explanation:

The Rational Zero Theorem can be used to list all possible rational zeros for a polynomial function. The possible zeros are the ratios of factors of the constant term to factors of the leading coefficient. In the case of the function f(x) = x^3 + 20x^2 - 16x - 14, the factors of the constant term (-14) are ±1, ±2, ±7, and ±14, and since the leading coefficient is 1, which has only one factor (±1), the possible rational zeros are simply the factors of the constant term. Therefore, the possible rational zeros are -1, -2, -7, -14, 1, 2, 7, 14.