Question

Use the rational zeros theorem to list all possible rational zeros of the following:

f(x) = -10x^3 + 9x^2 - 4x - 4
a) -4, -2, 1/2, 1, 2, 4
b) -3, -2, 1/2, 1, 2, 4
c) -4, -3, -2, 1/2, 1, 2, 3, 4
d) -4, -3, -2, 1/2, 1, 2, 4

Answer 1

The possible rational zeros of the given polynomial function are -4, -2, 1/2, 1, 2, and 4.

Step-by-step explanation:

The rational zeros theorem states that if a polynomial function has a rational zero, then it can be written in the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In the given polynomial function f(x) = -10x^3 + 9x^2 - 4x - 4, the leading coefficient is -10 and the constant term is -4. The factors of -10 are -1, 1, -2, 2, -5, and 5, and the factors of -4 are -1, 1, -2, and 2. Therefore, the possible rational zeros are:

1. -4/1
2. -2/1
3. 1/2
4. 1/1
5. 2/1
6. 4/1