Chapter 8.8, Problem 23PPE

To determine

To factor the expression $3w^4-2w^3+18w^2-12w$ .

Answer to Problem 23PPE

  $3w^4-2w^3+18w^2-12w=w\left(3w-2\right)\left(w^2+6\right)$

Explanation of Solution

Given:

  $3w^4-2w^3+18w^2-12w$

Calculation:

  $\begin{array}{l}3w^4-2w^3+18w^2-12w=w^3\left(3w-2\right)+6w\left(3w-2\right)\\ =\left(3w-2\right)\left(w^3+6w\right)\\ =w\left(3w-2\right)\left(w^2+6\right)\end{array}$