We started by looking at some current homework which involved factoring. For most of the problems they started with a quartic or cubic equation and then factored into a quadratic and one or two other terms.
Cubic equations can have three solutions, quartic equations can have four.
Talked a little about one application of imaginary numbers since we saw complex numbers in some solutions. And went into more detail about how to do calculations with them.
Talked about fractional exponents for a bit and how to work with them. Also about logarithms. The base being 10 if no other base is shown.
Fractional exponents are almost always easier to work with than ‘cube roots’, ‘fourth roots’ etc. Square roots aren’t too bad but still can be harder to manipulate in some cases.
Last problem we worked on was a three dimensional volume of a cone with the top cut off. Looked at the application of similar triangles and the proportionality of the sides.