Chapter 8.5, Problem 52PPE

To determine

To calculate: The factor of $d^2+30d-64$

Answer to Problem 52PPE

  $(d-2)(d+32)$

Explanation of Solution

Given information: The expression $d^2+30d-64$

Calculation:

  $\begin{array}{l}{d}^2+30d-64\\ =d^2+(32-2)d-64[\because 64=32\times 2\text{and}\text{ 30}=32-2]\\ =d^2+32d-2d-64\\ =(d^2+32d)-(2d+64)\\ =d(d+32)-2(d+32)\\ =(d-2)(d+32)\end{array}$

Thus, $d^2+30d-64=(d-2)(d+32)$