Chapter 8.8, Problem 20PPE

To determine

To find:The factorization of $18h^3+45h^2-8h-20$

Answer to Problem 20PPE

  $(3h+2)(3h-2)(2h+5)$

Explanation of Solution

Given information:The expression $18h^3+45h^2-8h-20$

Calculation:

  $\begin{array}{l}18h^3+45h^2-8h-20\\ =(18h^3+45h^2)-(8h+20)\\ =9h^2(2h+5)-4(2h+5)[\text{factoring out the GCF of each of the two terms]}\\ =(9h^2-4)(2h+5)[\text{factoring out the common term }(2h+5)]\\ $ =\{{(3h)}^2-{(2)}^2\}(2h+5)$=(3h+2)(3h-2)(2h+5)[\because a^2-b^2=(a+b)(a-b)]\end{array}$

Thus, $18h^3+45h^2-8h-20=(3h+2)(3h-2)(2h+5)$