Question

Which expression is equivalent to x³ - x² - 14x + 24?

A) (x-2)(x - 3)(x + 4)
B) (x-2)(x+3)(x-4)
C) (x + 2)(x - 3)(x-4)
D) (x + 2)(x+3)(x + 4)

Answer 1

A. ( x - 2 )( x - 3 )(x + 4 )

Explanation:

x³ - x² - 14x + 24

1. Use the rational root theorem

`= (x - 2) (x ^(3) -x^(2) - 14x + 24)/(x - 2)`

2.
`\frac{ {x}^(3) - {x}^(2) - 14x + 24 }{x - 2} = {x}^(2) + x - 12`

= ( 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 )