Just because it looks like x = 7 is an x-intercept, doesn’t mean that it is. Maybe the x-intercept is very close to 7 (like 7.001)—you would not be able to tell this from the graph. As a result, you must test what might be a factor using the factor theorem.

In this case you have determined that x − 7 is a factor. Isabel needs to perform the following division to determine another factor:

That is going to be a lot of work. Fortunately, there is a faster, mathematically equivalent process, called synthetic division. Watch Synthetic Division to see how the process works.

Self-Check 1

Complete questions 4.a., 4.b., and 4.c. on page 124 of the textbook.

4.  
   1. Answer
   2. Answer
   3. Answer

Try This 2

Back to Isabel and the whooping cranes. Previously it was determined that x − 7 is a factor of −x4 + 12x3 − 37x2 + 6x + 56. Use long division or synthetic division, whichever you prefer, to determine another factor. Continue factoring until you have written −x4 + 12x3 − 37x2 + 6x + 56 as the product of four binomial factors.

Save your responses in your course folder.