MATH1050: Polynomial Division
Instructor: Laura Strube
Name:
Student ID:
Answer the questions in the spaces provided or copy the questions neatly on
your own paper
For each of the following,
(a) Calculate the quotient using standard polynomial division. Remainders should be
expressed as the appropriate fractions.
(b) Check your work using polynomial multiplication (if your originial solution was incorrect you should rework the problem)
(c) Calculate the quotient using synthetic division [your synthetic division solution should
match your standard polynomial division].
It is very important that you show your work for these problems. While the
ability to arrive at a correct solution is important, a solid understanding of how
to do the calculation is equally important. I will be grading for both skills.
1
1. (5 points)
7x4 −12x3 −3x2 −x−1
x−2
(a) Calculate the quotient using standard polynomial division
(b) Check your work using polynomial multiplication
(c) Calculate the quotient using synthetic division
2. (5 points)
7x4 +23x3 +7x2 +4x+5
x+3
(a) Calculate the quotient using standard polynomial division
(b) Check your work using polynomial multiplication
(c) Calculate the quotient using synthetic division
3. (5 points)
4x3 +2x2 +6x+8
2x+4
(a) Calculate the quotient using standard polynomial division
(b) Check you work with polynomial multiplication
(c) Calculate the quotient using synthetic division
4. (5 points)
x6 +4x5 +9x4 +15x3 +13x2 +8x+1
x2 +x+1
(a) Calculate the quotient using standard polynomial division
(b) Check your work using polynomial division
Bonus Question - This problem is worth an additional 5 points added onto
your homework score - The entire problem must be completed to earn the
points
5. (5 points)
2x4 +7x3 +7x2 +4x+4
2x+4
(a) Calculate the quotient using standard polynomial division
(b) Check your work using polynomial division
(c) Calculate the quotient using synthetic division