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Synthetic Division Review

Examples:
(1.) f ( x) = x6 + 7x5 + 12x4 −14x3 − 59x2 − 57x −18
a. Possible Rational Zeros:

b. Descartes’ Rule of Signs :
f (−x) = x6 − 7x5 +12x4 + 14x3 − 59x2 + 57x −18

c. Synthetic Division :

d. x = 2, − 1,−1,−1,−3,−3

(2.) f ( x) = −4x3 + 15x2 − 8x − 3
a. Possible Rational Zeros:

b. Descartes’ Rule of Signs :
f (−x) = +4x3 + 15x2 + 8x − 3

c. Synthetic Division :

d. x = −1/4,1,3

(3.) f ( x) = x4 − 4x3 + 8x2 −16x + 16
a. Possible Rational Zeros:

b. Descartes’ Rule of Signs :
f (−x) = x4 + 4x3 + 8x2 + 16x + 16

c. Synthetic Division :

d. x = ± 2i, 2 ( multiplicity of 2)

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