Chapter 4.5, Problem 17WE

To determine

To factor thepolynomial.

Answer to Problem 17WE

The value of polynomial is $\left(t-3\right)\left(t^2+3t+9\right)$ .

Explanation of Solution

Given information:

  $t^3-27$

Calculation:

The polynomial can be obtained as

  $\begin{array}{l}{t}^3-27\\ ={\left(t\right)}^3-{\left(3\right)}^3\left[\text{use sum and differnce of cubes}\right]\\ =\left(t-3\right)\left(t^2+3t+9\right)\left[\text{since},\left(a^3-b^3\right)=\left(a-b\right)\left(a^2+ab+b^2\right)\right]\end{array}$

Hence,

The value of polynomial is $\left(t-3\right)\left(t^2+3t+9\right)$ .