Chapter 11.10, Problem 8MRE

To determine

To find: The factor completely.

Answer to Problem 8MRE

The factors are $t\left(t-9\right)\left(t+5\right)$ .

Explanation of Solution

Given:

The given expression is,

  $t^3-4t^2-45t$

Calculation:

The expression is simplified as,

  $\begin{array}{c}{t}^3-4t^2-45t=t\left(t^2-4t-45\right)\\ =t\left(t^2-9t+5t-45\right)\\ =t\left[t\left(t-9\right)+5\left(t-9\right)\right]\\ =t\left(t-9\right)\left(t+5\right)\end{array}$

Therefore, the factors are $t\left(t-9\right)\left(t+5\right)$ .