In order to find the other factor, we can use polynomial long division. We divide x^3 - 5x^2 - 2x + 24 by x - 3:
x^2 - 2x - 8
______________________
x - 3 | x^3 - 5x^2 - 2x + 24
- (x^3 - 3x^2)
_______________
- 2x^2 - 2x
+ (2x^2 - 6x)
_______________
- 4x + 24
- (-4x + 12)
_______________
12
The remainder is 12, which means that x - 3 is a factor of x^3 - 5x^2 - 2x + 24.
From the division, we obtain the quotient as x^2 - 2x - 8.
Thus, the other factor is x^2 - 2x - 8.
None of the given options (x-2, x+4, x^2-8x+22, x+2) are the correct factor. The correct factor is x^2 - 2x - 8.
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