X^3-5x^2-2x+24 factorize

Answer: (x-2) (x-3) (x-4)

Step-by-step explanation:

Use the rational root theorem to get started, then factor the remaining quadratic to find:

f (x) = x^3-5x^2-2x+24

f (2) = (2) ^3-5 (2) ^2-2 (2) + 24

f (2) = 0

i. e 2 is a root of f (x)

(x-2) is a factor

Now by dividing x^3-5x^2-2x+24by (x-2),

we get q (x) = x^2-7x+12

Since, q (x) is also a factor of x^3-5x^2-2x+24

Factorising x^2-7x+12

(x-4) (x-3)

So, all the factors of

x^3-5x^2-2x+24 are (x-4), (x-3) and (x-2)

(x + 2) (x - 3) (x - 4) = 0