Today's soundtrack is Air Supply: Ultimate Air Supply.
Nothing really exciting to report today. Spent the last half hour banging my head and trying to figure out how to factor (4x² + 4x + 3)² - 8 (4x²+4x+3) + 12. Finally I got it: I substituted 4x² + 4x + 3 for the variable a, then factored a² - 8a + 12, which gave me (a - 2) (a - 6). Then I substituted the expression back in, which gave me (4x² + 4x + 3 - 2) (4x² + 4x + 3 - 6). I grouped like terms, giving me (4x² + 4x + 1) (4x² + 4x - 3), then factored each of the bracketed expressions, resulting in the solution: (2x + 1)²(2x - 1)(2x + 3). I've now completed all the homework for unit 3.1! Next time, I'll be learning about solving quadratic equations by factoring.