…and polynomial division, too.
After teaching AP Calculus BC for almost seven years, I wonder whether there is any value in teaching Polynomial Division and Synthetic Division in PreCalculus.
So, in Calculus, you might have to integrate (or differentiate) a rational expression. You might want to use algebra to make an equivalent form of that so it is easier to differentiate. My school’s textbook recommends polynomial division for a problem like this but I think it’s better to use algebra: UseAlgebra
I feel it is much better to simply give students exercises wherein a little creative addition of forms of zero can be used to create the factors you want in the numerator. It keeps them on their toes as far as “chunking” and thinking in terms of factors.
*my apologies to people who know Latin for the appropriation of Cato the elder’s quote. I probably used the wrong case in there.