AFF Factoring to Find Zeros of Polynomials

Week of 12/22/14

Last week we extended our factoring prowess to analyze more sophisticated polynomial functions.

For example, we know that if we analyze p(x) below, we should first factor it (AFF!)  

In factored form, it will be clear that the first graph shown below does not match the given function. But the factored form will tell us the zeros we should expect to see.

In addition, last week we discussed the concepts of multiplicity.  We explored different graphs of polynomials that had repeated binomial factors linear factors raised to a power.  We can now analyze more complex behavior by inspecting the types of zeros (crossing or tangent).

We will discuss more graphing implications this week and after the holiday break.

 After the break we can also apply synthetic division as a solving tool.

Leftover goal which will be our focus this week

• Be able to make sense of word problems that lead to polynomial functions.         Then, persevere in solving them using factoring or other techniques.