Chapter 8.8, Problem 32PPE

To determine

To find: The factorization of $60y^4-300y^3-42y^2+210y$

Answer to Problem 32PPE

  $6y(10y^2-7)(y-5)$

Explanation of Solution

Given information: The expression $60y^4-300y^3-42y^2+210y$

Calculation:

  $\begin{array}{l}60y^4-300y^3-42y^2+210y\\ =6y(10y^3-50y^2-7y+35)[\text{factoring out the GCF 6}y\text{]}\\ =6y\{(10y^3-50y^2)-(7y-35)\}\\ =6y\{10y^2(y-5)-7(y-5)\}[\text{factoring out the GCF from each of the two terms]}\\ =6y(10y^2-7)(y-5)[\text{factoring out the common factor}(y-5)]\end{array}$

Thus, $60y^4-300y^3-42y^2+210y=6y(10y^2-7)(y-5)$