Question

F(x)=x cubed +3x squared -6x-8

Answer 1

Answer: x = {-4, -1, 2}

Step-by-step explanation:

        q                     p

F(x) = x³ + 3x² - 6x - 8

$\frac{p}{q} = +/- \frac{1, 2, 4, 8}{1}$

Possible rational roots are: +/- {1, 2, 4, 8}

F(1) = (1)³ + 3(1)² - 6(1) - 8

     =  1 + 3 - 6 - 8

     =  -10    Since the remainder is not 0, then x = 1 is not a root

F(-1) = (-1)³ + 3(-1)² - 6(-1) - 8

       = -1 + 3 + 6 - 8

       =  0   Since the remainder is 0, x = -1 is a root.

Use synthetic division to find the remaining factor:

x = -1  →  x + 1 = 0

-1  |  1     3     -6     -8

   |  ↓    -1     -2      8    

      1      2    -8      0

(x + 1)(x² + 2x - 8)  = 0

Next, factor the polynomial:

(x + 1)(x + 4)(x - 2)  = 0  

x + 1 = 0        x + 4 = 0         x - 2 = 0

x = -1              x = -4               x = 2