Section 3.2
Synthetic Division
Long Division of a polynomial
Example 1: Divide using Long Division.
a)
b)
12𝑥 3 −𝑥 2 −𝑥
3𝑥−1
3𝑥 4 −𝑥 3 −15
𝑥 2 +5
Section 3.2 Synthetic division
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c)
5𝑥 3 −6𝑥 2 −28𝑥−2
𝑥+2
Example 2: Use Synthetic Division to divide.
5𝑥 3 − 6𝑥 2 − 28𝑥 − 2
𝑥+2
Section 3.2 Synthetic division
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Example 3: Let 𝑓(𝑥) = −𝑥 4 + 3𝑥 2 − 4𝑥 − 5. Use the remainder theorem to find 𝑓(−3).
Section 3.2 Synthetic division
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Example 4: Decide whether the given number k is a zero of 𝑓(𝑥).
a) 𝑓(𝑥) = 𝑥 3 − 4𝑥 2 + 9𝑥 − 6; 𝑘 = 1
b) 𝑓(𝑥) = 𝑥 4 + 𝑥 2 − 3𝑥 + 1; 𝑘 = −1
Section 3.2 Synthetic division
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