Chapter 8.5, Problem 3LC

To determine

To calculate: The factor of $p^2+3p-40$

Answer to Problem 3LC

  $(p-5)(p+8)$

Explanation of Solution

Given information: The expression $p^2+3p-40$

Calculation:

  $\begin{array}{l}{p}^2+3p-40\\ =p^2+(8-5)p-40[40=8\times 5,3=8-5]\\ =p^2+8p-5p-40\\ =(p^2+8p)-(5p+40)\\ =p(p+8)-5(p+8)\\ =(p-5)(p+8)\end{array}$

To check,

  $\begin{array}{l}(p-5)(p+8)\\ =p^2+8p-5p-40[\text{by FOIL method]}\\ =p^2+3p-40\end{array}$

Thus, $p^2+3p-40=(p-5)(p+8)$