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Writing Polynomial Functions from Complex Roots

Question 3 • [INMT3] Integrated Math 3 Sem 1 (26-27)

Which equation is equivalent tof(x) = 16x4 – 81 = 0?

Answer
A
(4x² - 9)(4x² - 9) = 0
B
(4x² + 9)(4x² - 9) = 0
C
(4x - 9)(4x - 9) = 0
D
(4x + 9)(4x - 9) = 0

Explanation

Recognize 16x⁴ − 81 as a difference of squares: (4x²)² − 9². Using a² − b² = (a + b)(a − b), it factors as (4x² + 9)(4x² − 9), which is choice B.

AI-written and checked against the verified answer.

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