Identify all of the roots of the function. f(x) = x3 – 5x2 – 2x + 24

–2

–3

2

3

4

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)

the infinity sign

step-by-step explanation: