According to the rational root theorem, which of the following are possible roots of the polynomial function below? f(x) = 4x^3 - 6x^2 + 9x + 10

B, C, D, F

Step-by-step explanation:

The constant term is 10. It has divisors 1, 2, 5, 10.

The highest-degree term is 4x³. Its coefficient has divisors 1, 2, 4.

The rational root theorem tells you the possible rational roots will be one of the divisors of the constant term divided by one of the divisors of the the coefficient of the highest-degree term. (The roots may be positive or negative.)

Hence, possible rational roots include ...

... ±1/4, ±1/2, ±1, ±5/4, ±2, ±5/2, ±5, ±10

These show on your answer list as ...

-1/2

-2

5/4

5

Step-by-step explanation: