Factorize completely \(\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8}\)
A
x(x-5)2(x+2)
B
x(x-5)2(x-2)
C
x(x+5)2(x+2)
D
x2+52x+4
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8} = \frac{x(x^{2} + 3x - 10)}{2(x^{2} - 4)}\)
= \(\frac{x(x^{2} - 2x + 5x - 10)}{2(x - 2)(x + 2)}\)
= \(\frac{x(x - 2)(x + 5)}{2(x - 2)(x + 2)}\)
= \(\frac{x(x + 5)}{2(x + 2)}\)
Source: Myschool Past Questions Archive (Record #9794)