Question
i) \( 2 x^{3}-50 x= \)
Ask by Burns Garrett. in Ecuador
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(2x^3 - 50x = 2x(x - 5)(x + 5)\)
Solution
1. Extraemos el factor común \(2x\) de la expresión:
\[
2x^3 - 50x = 2x(x^2 - 25)
\]
2. Observamos que \(x^2 - 25\) es una diferencia de cuadrados, ya que se cumple que \(25 = 5^2\). Recordando que:
\[
a^2 - b^2 = (a - b)(a + b)
\]
aplicamos con \(a = x\) y \(b = 5\):
\[
x^2 - 25 = (x - 5)(x + 5)
\]
3. Sustituyendo en la expresión original:
\[
2x^3 - 50x = 2x(x - 5)(x + 5)
\]
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Simplify this solution Mind Expander
To solve the equation \(2x^3 - 50x = 0\), you can start by factoring out the common term. By taking out \(2x\), you get \(2x(x^2 - 25) = 0\). This factors further into \(2x(x - 5)(x + 5) = 0\). This gives us three solutions: \(x = 0\), \(x = 5\), and \(x = -5\). So, you’ve found your roots! In mathematics, understanding how to factor polynomials is crucial as it simplifies solving equations. It’s like finding the hidden treasures in a complex sea of numbers. Mastering this skill not only helps in algebra but also opens doors to calculus and beyond!
