x^4-2X^2-16x+32 factor

Need to factor this equation fully
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This is what I came up with unless the 4 is supposed to be a 3. x^4 - 2x² - 16x + 32 = (x^4 - 2x²) - (16x + 32) = x²(x² - 2) - 16(x - 2) = (x² - 16)(x² - 2)(x - 2)
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