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b) \( \left(2 x^{4}-5 x^{2}+16 x\right):(x-4) \)

Ask by Mcguire Perkins. in Spain
Mar 10,2025

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La división de \(2x^4 - 5x^2 + 16x\) entre \(x - 4\) da como resultado \(2x^3 + 8x^2 + 27x + 124\) con un resto de 496.

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The Deep Dive

To solve the polynomial division \( \left(2 x^{4}-5 x^{2}+16 x\right):(x-4) \) using synthetic division or long division is a fun challenge! First, arrange the polynomial in descending order. Notice the missing \(x^3\) term—remember to include a placeholder as \(0x^3\). After completing the division, you’ll end up with a quotient and possibly a remainder. This process helps to simplify complex expressions and understand polynomial behavior better! In practice, polynomial division is used in various fields such as computer science, engineering, and economics. It helps in finding roots of equations, optimizing functions, and even in coding algorithms to process polynomial data effectively. It’s fascinating how mathematical processes blend into real-world applications!

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