When you factor out the expression $x^2+1$, you factor out the term having the smallest exponent (which you did), and then you subtract that exponent...
I obtained a master's degree in mechanical engineering in May 2014.
Then I went on to join a master's programme in mathematics and obtained a master's degree in July 2016. I am currently a first year PhD student in mathematics. I love fountain pens and am a die hard fan of the Prince of Persia 2008 video game.