Chapter 8.5, Problem 3P

a.

To determine

To find:The factored form of the polynomial $n^2+9n-36$

Answer to Problem 3P

  $(n-3)(n+12)$

Explanation of Solution

Given information:The expression $n^2+9n-36$

Calculation:

  $\begin{array}{l}{n}^2+9n-36\\ =n^2+(12-3)n-36\\ =n^2+12n-3n-36\\ =(n^2+12n)-(3n+36)\\ =n(n+12)-3(n+12)\\ =(n-3)(n+12)\end{array}$

Thus, $n^2+9n-36=(n-3)(n+12)$

b.

To determine

To find: The factored form of the polynomial $c^2-4c-21$

Answer to Problem 3P

  $(c+3)(c-7)$

Explanation of Solution

Given information:The expression $c^2-4c-21$

Calculation:

  $\begin{array}{l}{c}^2-4c-21\\ =c^2-(7-3)c-21\\ =c^2-7c+3c-21\\ =(c^2-7c)+(3c-21)\\ =c(c-7)+3(c-7)\\ =(c+3)(c-7)\end{array}$

Thus, $c^2-4c-21=(c+3)(c-7)$