Chapter 14, Problem 51SGR

To determine

To calculate: The factors of the polynomial expression $t^2-5t-6$ .

Answer to Problem 51SGR

The factors of the polynomial expression $t^2-5t-6$ are $t-6\text{and}t+1$ .

Explanation of Solution

Given Information:

The polynomial expression is $t^2-5t-6$ .

Calculation:

The given polynomial expression is $t^2-5t-6$ .

Split $5t$ into two parts such that their product is equal to the product of $t^2$ and 6.

  $\begin{array}{c}{t}^2-5t-6=t^2-6t+t-6\\ =t\left(t-6\right)+1\left(t-6\right)\\ =\left(t-6\right)\left(t+1\right)\end{array}$

Hence, the factors of the polynomial $t^2-5t-6$ are $t-6\text{and}t+1$ .