Use the Factor Theorem to find a polynomial equation, of lowest possible degree, that has only the indicated roots.

3, -2, sqrt of 2, - sqrt of 2

"-" means negative

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The answer :

(x - 3)(x + 2)(x² - 2) = 0

so : (x² + 2x - 3x - 6)(x² - 2) = 0

so : (x² - x - 6)(x² - 2) = 0

so : (x^4 - 2x² - x^3 + 2x - 6x² + 12) = 0

so : x^4 - x^3 - 8x^2 + 2x +12 = 0

so the polynomial is : P(x) = x^4 - x^3 - 8x^2 + 2x +12

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