Synthetic Division Reminder!
A few examples of how it is done…
EX. 1
(1x4 – 4x3 – 7x2 + 34x – 24) ÷ (x + 3)
You set it up like this…
x+3=0
-3 -3
-3
1
x = -3
1
-4
-3
-7
21
34
-42
-24
24
-7
14
-8
0
Whatever number ends up in this
position is the remainder. With this
case, x + 3 divided into the
polynomial evenly.
Once you finish you put the
variable x back onto the
number starting one degree
lower that it was before.
In this case you start with x 3
because it was x4 before the
synthetic division.
So, the answer would be 1x3 – 7x2 + 14x – 8
Anytime you are missing exponents you
MUST add in the missing terms. So, if the
highest exponent is x5, then you should see an
x4, x3, x2, x, and a constant term.
EX. 2
(2x5 – 14x3 + 24x) ÷ (x – 3)
So, let’s rewrite it with those in there.
(2x5 + 0x4 – 14x3 + 0x2 + 24x + 0) ÷ (x – 3)
Now we can do the work.
3
2
0
6
2
6
-14 0
18 12
4
12
24 0
36 180
With
you add it
Whenthe
youremainder,
have a remainder,
onto
the answer
and putonto
it over
you add
the remainder
the
what
they
were
by.
answer
and
put dividing
it over what
they were dividing by.
60 180
So, the answer would be 2x4 + 6x3 + 4x2 + 12x + 60 +
180
( x  3)
Polynomial Division Reminder!
A few examples of how it is done…
Name______________________________________________________________Date_____________
Divide the following using both methods of Polynomial Division and Synthetic Substitution:
Polynomial Division
Synthetic Substitution
1. (x – 7x – 6) ÷ (x – 2)
(x – 7x – 6) ÷ (x – 2)
2. (4x2 + 5x + 8) ÷ (x + 1)
(4x2 + 5x + 8) ÷ (x + 1)
3. (x3 – 14x + 8) ÷ (x + 4)
(x3 – 14x + 8) ÷ (x + 4)
4. (x2 + 10) ÷ (x + 4)
(x2 + 10) ÷ (x + 4)
3
3
Divide the following using the method that you prefer! (Polynomial Division or Synthetic Substitution)
5. (10x4 + 5x3 + 4x2 – 9) ÷ (x + 1)
6. (x3 + 8x2 – 3x + 16) ÷ (x + 5)
7. (2x4 – 6x3 + x2 – 3x – 3) ÷ (x – 3)
8. (x4 – 6x3 – 40x + 33) ÷ (x – 7)
9. (4x4 + 5x3 + 2x2 – 1) ÷ (x + 1)
10. (-10x5 + 3x – 7) ÷ (x – 1)