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Warm Up
Homework Questions 3.1 part 2
1. Identify the vertex: f(x) = 2(x - 2)2 + 4
2. Identify the vertex: f(x) = 2x2 - 8x +12
3. FOIL: (1 + 3i)(-3 + 3i)
3.2 – Dividing Polynomials
Dividing a Polynomial
by a Polynomial
When setting up division whether long or synthetic, you
MUST add in a zero for any values missing as place holders.
Objective: TSW divide polynomials using
synthetic division and evaluate using the
remainder theorem.
Example 1: Divide using long division
When to use synthetic division
• Only used by linear divisors, form x – k.
• Divide by the opposite of k
• Used to evaluate, f(?), remainder theorem
• Used to find zeros
• Much easier than long division!
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Example 2 – Divide using synthetic division:
Example 3
0 x3
3
2
x − 4x2 + 6
x−4
x + 6x + 8x − 2
x+3
-3
1
6
8
-2
4
1
0
-4
0
6
Example 5: Evaluate
for f(4).
Example 4
4 x 3 + 8 x 2 − 25 x − 50 divided by x + 2
-2
0x
4
4
8
-25
-50
Example 6 – Determine if k=2 is a zero
of:
Now let’s use the remainder theorem which
says, we can use synthetic division and the
answer will be the remainder, use the number listed
in the parenthesis (this is the k).
Example 7:
k=-3 a zero?
; is
Something is a zero (root or solution) to a
polynomial if you get no remainder when you
use synthetic division.
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Example 8:
k= 1+3i a zero?
; is
Homework
3.2 page 326 1-17 odds,27-35 odds,41-45 odds
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