Chapter 8.6, Problem 44PPE

To determine

To calculate: The factorization of $36p^2+114p-20$

Answer to Problem 44PPE

  $2(6p-1)(3p+10)$

Explanation of Solution

Given information: The expression $36p^2+114p-20$

Calculation:

  $\begin{array}{l}36p^2+114p-20\\ =2(18p^2+57p-10)\\ =2\{18p^2+(60-3)p-10\}\\ =2\{18p^2+60p-3p-10\}\\ =2\{(18p^2+60p)-(3p+10)\}\\ =2\{6p(3p+10)-1(3p+10)\}[\text{factoring out the GCF from each of the two terms]}\\ =2(6p-1)(3p+10)[\text{factoring out the common factor }(3p+10)]\end{array}$

Thus, $36p^2+114p-20=2(6p-1)(3p+10)$