Answer:
A. ( x - 2 )( x - 3 )(x + 4 )
Step-by-step explanation:
x³ - x² - 14x + 24
1. Use the rational root theorem
[tex] = (x - 2) \frac{x ^{3} -x^{2} - 14x + 24}{x - 2} [/tex]
2. [tex] \frac{ {x}^{3} - {x}^{2} - 14x + 24 }{x - 2} = {x}^{2} + x - 12[/tex]
= ( x - 2 )( x² + x - 12 )
3. Factor x² + x - 12 : ( x -3 )( x + 4)
= ( x - 2 )( x - 3 )(x + 4 )
Solution :
= ( x - 2 )( x - 3 )(x + 4 )
