Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 779: 72

$(y^{2}+6)(\sqrt 2y-1)(\sqrt 2y+1)$

Step 1: Let u=$y^{2}$ $=2u^{2}+11u-6$ Step 2: Factor $2u^{2}+11u-6$ =(u+6)(2u-1) Step 3: Substitute back $u=y^{2}$ $=(y^{2}+6)(2y^{2}-1)$ Step 4: Factor $2y^{2}-1$ $=(\sqrt 2y-1)(\sqrt 2y+1)$ Step 5: Place all of the factors into one $(y^{2}+6)(\sqrt 2y-1)(\sqrt 2y+1)$