1. Dividing Polynomials (SYNTHETIC Division)
NOTES 6.3 B
Dividing Polynomials
(SYNTHETIC Division)

2. EX – Synthetic division (5x³ -13x² +10x -8) / (x-2)
Opposite
of number in
divisor 2 10 -6 8 5 -3 4
5x² -3x + 4

3. EX – Synthetic division (3x³ -4x² +2x -1) / (x+1)
Opposite
of number in
divisor -1 -3 +7 -9 3 -7 9
-10
3x x R-10

4. A Couple of Notes
Use synthetic division when the coefficient in front of x is 1
(x- 2) (2x-3)
YES NO

5. The Remainder Theorem
If a polynomial f(x) is divided by (x - a), the remainder is the constant f(a).

6. The Remainder Theorem Example # 1
Find the remainder: (x2 + 3x - 12) / (x - 4) (4)2 + 3(4) – 12 = = 16  R 16

7. The Remainder Theorem Example # 2
Find the remainder: (x4 – 5x2 + 4x + 12) / (x + 4) (-4)4 - 5(-4)2 + 4(-4) + 12 = 256 – 80 – = 172  R172