Remainder theorem of polynomials

The  exercise appears under the Algebra II Math Mission. This exercise applies the remainder theorem about polynomials to specific problems.

Types of Problems
There are three types of problems in this exercise:


 * 1) ''Determine the unknown to make something a factor: This problem provides a polynomial and a binomial that needs to be a factor of the polynomial. The student is expected to find the correct value of c that will work.Rtop1.png
 * 2) Apply the remainder theorem to find the remainder: This problem states that a particular polynomial is divided by a linear binomial and asks for the remainder. The student is expected to find the remainder, and state whether the binomial expression was a factor of the polynomial.Rtop2.png
 * 3) Select whether or not it is a factor: This problem provides a polynomial and a proposed factor. The student is asked to determine whether or not the proposed factor is actually a factor or not.Rtop3.png

Strategies
Knowledge of the remainder theorem and other polynomials theorems are encouraged to ensure success on this exercise.
 * 1) The remainder theorem states that the numerical remainder when one divides p(x) by x-r, is just p(r).
 * 2) A corollary, the factor theorem, states that x-r being a factor of a polynomial is equivalent to p(r) evaluating to zero. Another motivation for calling these values zeroes.

Real-life Applications

 * 1) The remainder theorem provides a more efficient avenue for testing whether certain numbers are roots of polynomials.
 * 2) This theorem can increase efficiency when applying other polynomial tests, like the rational roots test.