Which of the following is a factor of x^3−5x^2−2x+24, given that x−3 is one of the linear factors?

x-2
x+4
x^2-8x+22
x+2

1 answer

In order to find the remaining factor, we can use polynomial long division.

x^2 + 6x + 8
______________________
x - 3 | x^3 - 5x^2 - 2x + 24
x^3 - 3x^2
_______________________
- 2x^2 - 2x
- 2x^2 + 6x
__________________
4x + 24
4x - 12
______________
36

So, x^3 - 5x^2 - 2x + 24 = (x - 3)(x^2 + 6x + 8) + 36

Therefore, the remaining factor is 36.

Among the given options, none of them are equal to 36. Thus, none of the given options is a factor of x^3 - 5x^2 - 2x + 24.