Which of the following values are zeros of f (x) = x³ - 8x² - 5x + 84? Select all that apply.

The answer to your question is: - 3 and 7

Step-by-step explanation:

To know if a value is a zero of the polynomial is necessary to find the prime factors of 84.

84 2

42 2

21 3

7 7

1

Then, the possible values are ±1, ±2, ±3, ±7.

After that, we evaluate each value in the polynomial, if the result is zero, that number is a root of the polynomial.

Example

(-3) ³ - 8 (-3) ² - 5 (-3) + 84

-27 - 72 + 15 + 84

- 99 + 99 = 0

Then, - 3 is a zero of the polynomial

(7) ³ - 8 (7) ² - 5 (7) + 84

343 - 392 - 35 + 84

427 - 427 = 0

Then, 7 is a zero of the polynomial