2. Let’s look at how to do this
using the example:
( 5x
#1
4
− 4 x + x + 6 ) ÷ ( x − 3)
2
In order to use synthetic division these
two things must happen:
#2 The divisor must
There must be a
coefficient for
have a leading
every possible
coefficient of 1.
power of the
variable.

3. Step #1: Write the terms of the polynomial so
the degrees are in descending order.
5x + 0x − 4x + x + 6
4
3
2
Since the numerator does not contain all the powers of x,
you must include a 0 for the x 3 .

4. Step #2: Write the constant a of the divisor
x- a to the left and write down the
coefficients.
Since the divisor = x − 3, then a = 3
5x
4
0x
3
−4 x
2
+ x +6
↓
3
↓
↓
↓
↓
5
0
−4
1
6

5. Step #3: Bring down the first coefficient, 5.
3
5 0 −4 1 6
↓
5
Step #4: Multiply the first coefficient by r (3*5).
3
5
0
↓ 15
5
−4 1 6

6. Step #5: After multiplying in the diagonals,
add the column.
Add the
column
3
5 0 −4 1 6
↓ 15
5 15

7. Step #6: Multiply the sum, 15, by r; 15g
3=15,
and place this number under the next coefficient,
then add the column again.
3
Add
5 0 −4 1 6
↓ 15 45
5 15 41
Multiply the diagonals, add the columns.

8. Step #7: Repeat the same procedure as step #6.
3
5
Add
Columns
0
Add
Columns
−4
1
Add
Columns
Add
Columns
6
↓ 15 45 123 372
5 15 41 124 378

9. Step #8: Write the quotient.
The numbers along the bottom are
coefficients of the power of x in
descending order, starting with
the power that is one less than that
of the dividend.

10. The quotient is:
378
5x + 15x + 41x + 124 +
x−3
3
2
Remember to place the
remainder over the divisor.

11. Try this one:
1) (t 3 − 6t 2 + 1) ÷ ( t + 2)
−2
1 −6 0
1
−2 16 −32
1 −8 16 −31
31
Quotient = 1t − 8t + 16 −
t+2
2