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8 September, 15:15

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

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  1. 8 September, 15:21
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    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.
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