1. Divide by x - 1 Synthetic Division: a much faster way! 5. 1. 2. 6. 3.
The answer is x + 6 with a remainder of 12. 4.

2. You try: Use synthetic division to divide. Answer: 5x2 - 10x + 26 - 44

3. The remainder is 0, which means that x-3 is a factor of
The Factor Theorem:
Let f(x) be a polynomial.
a. If f(c) =0, then x-c is a factor of f(x).
b. If x-c is a factor of f(x), then f(c) = 0.
Example 4: Solve the equation 2x3 – 3x2-11x + 6 = 0 given that 3 is a zero of f(x) = 2x3 -3x2-11x + 6.
Step 1: Use synthetic division and solve. 3|
The remainder is 0, which means that x-3 is a factor of
2x3 -3x2-11x + 6

4. What are the factors of 2x3 -3x2-11x + 6?
Using synthetic division, we found the factors to be (x-3)(2x2+ 3x-2) =0.
Finish factoring:
(x-3) (2x-1) (x+2) =0
Find the x- intercepts.
X=3, x=1/2, x=-2
The solution set is {-2, 1/2, 3}

5. You try: f(x)= 15x3+14x2 -3x -2=0, given that -1 is a zero of f(x), find all factors.
Answers:
-1|
Factors: (x+1) (15x2 –x -2)=0
(x+1) (5x-2)(3x+1)=0
x = -1, x= 2/5, x = -1/3
Solution Set {-1, -1/3, 2/5}

6. Summary:
Explain how the synthetic division can be used to determine if x-1 is a factor of
x3 -2x2 – 11x + 12.