How can one simplify the following ?
In this case one can either use long division or synthetic division.
Long Division :
Answer:
with a remainder of 169.
Synthetic Division :
• special case of long division when the divisor is a linear factor
Answer:
with a remainder of 169.
Most of the time when synthetic division is introduced to
students, they are told here is how it works and so just follow all the steps
and you will get the answer. The students do not understand why synthetic
division works or where is comes from, they are just able to compute it. So how
can we as future teachers be capable to explain synthetic division to our
students and related it to long division?
The numbers in red represent the connection from long
division to synthetic division. When teaching, one can explain to the students
the corresponding numbers in this manner.
Let’s try another example Simplify :
Long Division :
Answer: 
with a
remainder of
Synthetic Division : Since we are dividing by
we need to consider that by shift everything
over as shown below.
Answer: 
with a
remainder of
Now let’s try to simplify the following as we did
previously :
Long division :
Answer: 
with a
remainder of 
Synthetic division :
Answer: 
with a
remainder of 
Homework: Simplify the following using both long division
and synthetic division, state how synthetic division would work in this case.
