Chapter 4.4, Problem 18E

To determine

To find: The number of possible positive real zeros and the number of possible negative real zeros for function $f\left(x\right)=x^3-2x^2-8x$ . Then determine the rational zeros.

Answer to Problem 18E

Possible zeros: $\pm 1\text{, }\pm \text{2, }\pm 4\text{, }\pm 8$

  $x=0,-2,4$

Explanation of Solution

Given information: $f\left(x\right)=x^3-2x^2-8x$

Calculation:

You can factor out an x which gives you

  $x^2-2x-8$

Possible zeros for this are: $\pm 1\text{, }\pm \text{2, }\pm \text{4, }\pm \text{8}$

  $x^3-2x^2-8x=x\left(x^2-2x-8\right)\to x\left(x-4\right)\left(x+2\right)$

Zeros: $x=0,-2,4$