Factorize completely \(\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8}\)

  • A \(\frac{x(x-5)}{2(x+2)}\)
  • B \(\frac{x(x-5)}{2(x-2)}\)
  • C \(\frac{x(x+5)}{2(x+2)}\)
  • D \(\frac{x^2+5)}{2x+4)}\)
jamb 2010mathematics

The correct answer is C. \(\frac{x(x+5)}{2(x+2)}\)

\(\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8} = \frac{x(x^{2} + 3x - 10)}{2(x^{2} - 4)}\)

= \(\frac{x(x^{2} - 2x + 5x - 10)}{2(x - 2)(x + 2)}\)

= \(\frac{x(x - 2)(x + 5)}{2(x - 2)(x + 2)}\)

= \(\frac{x(x + 5)}{2(x + 2)}\)

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