Okay folks, it's time that you put your thinking caps on. We observed some interesting results in class today when it came to dividing polynomial functions by expressions that were not generated by the roots of the functions. To prove these results to be true for every case, we will have to remember a few things about division, and especially about remainders.
When dividing a number, say 79, by another number, say 7, we get a remainder of 2. If I were to write this statement differently then I could say that 79 = (7)(11) + 2 (you should try out and verify what I am saying here).
Now see if this same kind of statement works for an actual example of a polynomial that is divided by an expression that is not a factor. You can use the two examples from class and try and write the statement I showed you but instead using the polynomials.
After this the work gets interesting and tricky. Try and write a similar statement for a random polynomial f(x) being divided by (x-a) and you can call the remainder r. bring to class anything and everything that occurs to you
NOTE: The class work that you have to complete are questions 1 and 2 from page 90 of your text book.
When dividing a number, say 79, by another number, say 7, we get a remainder of 2. If I were to write this statement differently then I could say that 79 = (7)(11) + 2 (you should try out and verify what I am saying here).
Now see if this same kind of statement works for an actual example of a polynomial that is divided by an expression that is not a factor. You can use the two examples from class and try and write the statement I showed you but instead using the polynomials.
After this the work gets interesting and tricky. Try and write a similar statement for a random polynomial f(x) being divided by (x-a) and you can call the remainder r. bring to class anything and everything that occurs to you
NOTE: The class work that you have to complete are questions 1 and 2 from page 90 of your text book.
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