Answer:
Roots are -2, 3, and 4
Step-by-step explanation:
Let's use the rational roots test.
Starting with the constant term (24), the roots are 1, 2, 3, 4, 6, 8, 12, and 24 (both positive and negative).
Starting with 2.
8 - 20 - 4 + 24 = 8 (so 2 is not a root).
Let's try 3.
27 - 45 - 6 + 24 = 0 (so 3 is a root). (x-3) is a factor.
Now we can divide x3-5x2-2x+24 by x-3 to get a polynomial.
x3-5x2-2x+24 / x-3
x2 - 2x - 8 = (x-4)(x+2)
