Question

If x = 1 is a zero of the polynomial function f(x) = 3x3 − 8x2 + 3x + 2, which of the following is another zero of f(x)?

Answer 1

The given polynomial is
f(x) = 3x³ - 8x² + 3x + 2

Because x = 1 is a zero, therefore (x-1) is a factor.
Perform synthetic division.

1 | 3 -8 3 2
3 -5 -2
------------------
3 -5 -2 0

Therefore
f(x) = (x - 1)(3x² - 5x - 2)

Factorize 3x² - 5x - 2.
3x² - 5x - 2 = (3x + 1)(x - 2)

The remaining zeros are x = -1/3, x = 2.

Answer:
-1/3 is a zero
2 is a zero

Select the correct answer from your given choices.