To determine which of the given options is a linear factor of the expression \( x^4 - 8x^2 - 9 \), we can evaluate the expression at the potential roots from the options provided: \( x - 2 \), \( x - 1 \), and \( x - 3 \).
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Test \( x = 2 \): \[ f(2) = 2^4 - 8(2^2) - 9 = 16 - 32 - 9 = -25 \quad (\text{not a root}) \]
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Test \( x = 1 \): \[ f(1) = 1^4 - 8(1^2) - 9 = 1 - 8 - 9 = -16 \quad (\text{not a root}) \]
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Test \( x = 3 \): \[ f(3) = 3^4 - 8(3^2) - 9 = 81 - 72 - 9 = 0 \quad (\text{is a root}) \]
Since \( f(3) = 0 \), \( (x - 3) \) is a linear factor of the expression \( x^4 - 8x^2 - 9 \).
Therefore, the correct answer is: \[ (x - 3) \]