IM Alg2.2.15 Lesson: The Remainder Theorem
What do you notice? What do you wonder?
A. B. C.
Consider the polynomial function where is an unknown real number. If is a factor, what is the value of? Explain how you know.
Here are some diagrams that show the same third-degree polynomial, , divided by a linear factor and by a quadratic factor.
What is the remainder of each of these divisions? 
For each division, how does the degree of the remainder compare to the degree of the divisor?
Could the remainder ever have the same degree as the divisor, or a higher degree? Give an example to show that this is possible, or explain why it is not possible.
Which of these polynomials could have as a factor?
Select one of the polynomials that you said doesn’t have as a factor. Explain how you know is not a factor.
If you have not already done so, divide the polynomial by . What is the remainder?
List the remainders for each of the polynomials when divided by . How do these values compare to the value of the functions at ?