PLEASE EXPLAIN This is a college algebra problemThe answer i

PLEASE EXPLAIN. This is a college algebra problem.The answer is shown. Please explain or show work how to arrive at this answer.

\\ 10. List the potential rational zeros off(x) = 6x4 + 4x3 + 2x2-2. ±1, ± 2, ± 3, ± 6, ± ±1, ± 2, ± , ±,±1 6/ 3, ±6, ±4, ±3, ±2, ±3, ± 4, ± 1, ± 2, ±3 ±6, ±3, ±2, ±4, ± 1, ± 2, ± 3, ±4,±6 ±6, ±3, ± 2, ±3, ± 1, ±2 ± , ±, ±, ±, ± 1, ± 2, ± 3 36 13 O 3-2 37 2 2 2 2 1-2-23 1-1 6-3 12 17 23 23 1 3 1-6 1-3 1-2 12 17 1-3-2-2-2 3-6 2, 2, 14 13 13 13 1 16 16 1-6 1-6 08

Solution

Rational Roots Test

constant term is 2 with factor 1, 2

Leading coefficient = 6 with factor 1, 2 , 3

Possible rational roots : +/- 1 ,+/- 1/2, 1+/- 1/3 , +/- 1/6 , +/- 2/1 +/- 2/3

2nd last Option