𝑓(𝑥) = 6𝑥^3 − 3𝑥^2 + 4𝑥 − 4 and 𝑔(𝑥) = 9𝑥^2 + 𝑥 − 1. What is 𝑓(𝑥) − 𝑔(𝑥)? Show all of your steps and write your final answer in factored form.
f(x) - g(x) = 6 x³ - 3 x² + 4 x - 4 - ( 9 x² + x - 1 ) =
6 x³ - 3 x² + 4 x - 4 - 9 x² - x + 1 =
6 x³ - 3 x² - 9 x² + 4 x - x - 4 + 1 =
6 x³ - 12 x² + 3 x - 3 =
3 ( 2 x³ - 4 x² + x - 1 )
This is the simplest form because 2 x³ - 4 x² + x - 1 cannot be factorized.