Chapter 8.8, Problem 27P

Factor completely.

$30b^4-45b^3-10b^2+15b$

To determine

To find: The factorization of $30b^4-45b^3-10b^2+15b$

Answer to Problem 27P

  $5b(3b^2-1)(2b-3)$

Explanation of Solution

Given information: $30b^4-45b^3-10b^2+15b$

Calculation:

  $\begin{array}{l}30b^4-45b^3-10b^2+15b\\ =5b(6b^3-9b^2-2b+3)\\ =5b\{(6b^3-9b^2)-(2b-3)\}\\ =5b\{3b^2(2b-3)-1(2b-3)\}\\ =5b\{(3b^2-1)(2b-3)\}\\ =5b(3b^2-1)(2b-3)\end{array}$

Thus, $30b^4-45b^3-10b^2+15b=5b(3b^2-1)(2b-3)$