Divide polynomials by polynomials with remainders

The  exercise appears under the Algebra II Math Mission. This exercise practices rewriting expressions of the form $$\frac{a(x)}{b(x)}$$, where $$a$$ is a polynomial $$b$$ is a linear binomial, in the form $$\frac{q(x)+r(x)}{b(x)}$$, where $$q$$ and $$r$$ are polynomials and the degree of $$r$$ is less than the degree of $$b$$.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the quotient and remainder: This is a division problem involving two polynomials. The student is expected to correctly perform the division then type the quotient and remainder in the text boxes below.Divide polynomials by polynomials with remainders.PNG

Strategies
Knowledge of division with polynomials are encouraged to ensure success while doing this exercise.
 * 1) Some of the problems can be done with synthetic division. However, there are also problems that will require formal long division because of division by non-linear polynomials.

Real-life Applications

 * 1) An ability to manipulate expressions is used in the calculus to make formulas easier to perform calculus on.