Use the remainder theorem and the factor theorem to determine whether (y - 3) is a factor of (y4 + 2y2 - 4).

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.