Polynomials Unit Diving Polynomials Using Synthetic Division

1. Synthetic Division
Algebra 2 CP

2. Synthetic Division
 A trick for dividing polynomials
 Helps us solve for the roots of polynomials
 Only works when we divide by 1st
degree
(linear) polynomials
)2()11183( 24
−÷+−− xxxx
Exponent can’t be larger than 1!

3. Synthetic Division
)24()1152( 24
−−÷−+ xxxx
)2()11183( 24
−÷+−− xxxx

4. Your Turn
 On your Synthetic Division Notes packet,
complete problems 1 – 5.
 Decide if it’s possible to use synthetic division to
divide the two polynomials
1. Yes 2. Yes 3. No 4. No 5. No

5. Division Vocab Review
Dividend Divisor
2)3()65( 2
+=+÷++ xxxx
Quotient

6. Preparing for Synthetic
Division
 Can only be used when the divisor is in the
form:
 To divide, you will need the constant term of
your divisor: set your divisor equal to 0 and
solve!
x – c

7. Preparing for Synthetic
Division, cont.
 Polynomials need to be written in expanded,
standard polynomial form.
 For the polynomial to be expanded sequentially,
ALL terms must be listed
 AKA: If you’re missing terms, they must be filled in
with “place holders.”

8. Preparing for Synthetic
Division, cont.
xxx 273 35
−+
+−+++ xxx 273 35
020703 2345
+−+++ xxxxx

9. Your Turn
 On your Synthetic Division Notes packet, write
the dividend in expanded standard polynomial
form for problems 6 – 10.
6.
7.
8.
9.
10.

10. *Synthetic Division Steps
 Example Problem:
)2()11183( 24
−÷+−− xxxx

11. Prep Step
 Linear Divisor?
 x – 2
 Dividend in Expanded Standard Polynomial
Form?
 3x4
– 8x2
– 11x + 1
 3x4
+ – 8x2
– 11x + 1
 3x4
+ 0x3
– 8x2
– 11x + 1

12. Step 1
2
Write the constant value of the divisor (c) here.

13. Step 2
2
Write all the coefficients of the expanded
dividend here.
3 0 -8 -11 1

14. Step 3
2
“Drop” the 1st
coefficient underneath the line.
3 0 -8 -11 1
3

15. Step 4
2
Multiply “c” by the last value underneath the line.
Write their product just underneath the next
coefficient.
3 0 -8 -11 1
6
3

16. Step 5
2
Add together the numbers in that column and
write their sum underneath the line.
3 0 -8 -11 1
6
3 6

17. Step 6
2
Multiply “c” by the last value underneath the line.
Write their product just underneath the next
coefficient.
3 0 -8 -11 1
6 12
3 6

18. Step 7
2
Repeat steps 5 and 6 until a number appears in
the box underneath the last column.
3 0 -8 -11 1
6 12 8 -6
3 6 4 -3 -5

19. Step 8 – Naming the Quotient
2
In the last row are the coefficients of the quotient
in decreasing order. The quotient is one degree
less than the dividend.
3 0 -8 -11 1
6 12 8 -6
3 6 4 -3 -5

20. Step 8 – Naming the Quotient
3 6 4 -3 -5
The number in the box is the remainder.
=−÷+−− )2()11183( 24
xxxx

21. Your Turn
 On your Synthetic Division Notes packet,
solve for the quotient of problems 11 – 14
using synthetic division
11.
12.
13.
14.