I didn't "figure" that out. The given expression involved x4 so I knew it must be the square of a quadratic. The most general quadratic is ax2+ bx+ c. Then I saw that, in order to get "x4" and "+ 1" I must have a= 1, c= 1. I still did not know what b was so I left that in. I did not know that b was not 0, just that there was no reason to assume it wasn't!