Synthetic Division of Polynomials

We started by looking  at long division and synthetic division of polynomials.

Long division was familiar, synthetic division was new.

Synthetic division can be faster and less written work, but is more straightforward with certain conditions. You can use one method to check the other.

There is a decent explanation here, but with a mistake in the final example.

http://www.mesacc.edu/~scotz47781/mat120/notes/divide_poly/synthetic/synthetic_division.html

The ‘test zero’ goes on the outside. If you are dividing by (x-2), the test zero is 2, if you are dividing by x+6, the test zero is -6, etc. The test zero is the number that makes the denominator zero when you plug it in.

Synthetic division is straightforward when the coefficient for the variable in the denominator is of the form x + a and the leading coefficient of the numerator’s first term is 1.

Wikipedia describes how you can use it when things get more complicated, but I would probably just use long division if that is the case.

We then looked at some graphing of equations and inequalities. To find the x-coordinate of the vertex of a parabola you use -b/2a.

Also simplified some expressions.