Question
j) \( 2 x^{3}-32 x= \)
Ask by Floyd Harris. in Ecuador
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
La expresión \(2x^{3} - 32x\) se puede factorizar como \(2x(x - 4)(x + 4)\).
Solution
1. Extraer el factor común \(2x\):
\[
2x^3 - 32x = 2x(x^2 - 16)
\]
2. Reconocer que \(x^2 - 16\) es una diferencia de cuadrados, ya que
\[
x^2 - 16 = x^2 - 4^2
\]
y aplicar la fórmula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
obteniendo:
\[
x^2 - 16 = (x - 4)(x + 4)
\]
3. Sustituir en la factorización:
\[
2x(x^2 - 16) = 2x(x - 4)(x + 4)
\]
La expresión factorizada es:
\[
2x(x - 4)(x + 4)
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
Let's first factor out the common term in the equation. You can rewrite it as \( 2x(x^2 - 16) \). From here, you can further factor it into \( 2x(x - 4)(x + 4) \). Now, you can solve for the roots by setting each factor equal to zero, leading to solutions: \( x = 0, x = 4, \) and \( x = -4 \)! To double-check your work, remember to substitute each root back into the original equation. This approach ensures you haven't missed any values or made simple miscalculations. If you get zero on both sides of the equation, you can be confident in your solutions!
