LESSON 4 – COMPARING METHODS – LONG DIVISION, AGAIN? Opening Exercise

OPENING EXERCISE, SOLVED

DISCUSSION  Looking back at some of the examples, there appears to be a lot of similarity between polynomial multiplication and arithmetic multiplication (multiplying numbers together).  Likewise, polynomial division appears to be very similar to arithmetic division, in that it “undoes” the process of multiplication.  Consider for a moment: We have been able to represent the multiplication polynomials in a few ways; once by distributing terms from one factor into the other, and again by doing the same through the use of a table.  So far, we have restricted division to also using the tabular method, but thinking back to elementary school arithmetic, is that really how you learned to divide? What other method should we be able to use?

THE LONG DIVISION ALGORITHM

LONG DIVISION ALGORITHM

MORE EXAMPLES (THINGS TO NOTE FIRST)

EXAMPLE 2 Use the long division algorithm to do the following division:

EXAMPLE 2, WORKED OUT

SO WHAT’S THE POINT..? The biggest takeaway from this lesson: Polynomials form a system analogous to the integers. The same operations that hold for integers hold for polynomials.

PRACTICE PROBLEMS (NOT THE PROBLEM SET) Solve all these problems with the long division algorithm. Time-permitting, check your work with the tabular method.