Since the factor is (y-3).... then we can say y - 3 = 0, therefore y = 3. Thus the root or zero is at 3, using that factor.
Now, is it a factor of y⁴ +2y² - 4 ?
using the Remainder Theorem, that is true only if f(3) = 0, let's check then,
f(y) = y⁴ +2y² - 4
f(3) = (3)⁴ +2(3)² - 4
f(3) = 81 + 54 - 4
f(3) = 131
since f(3) ≠ 0, then the factor with the root of "3" is not a factor of y⁴ +2y² - 4.
