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Synthetic Division Review
Examples:
(1.) f ( x) = x^{6} + 7x^{5} + 12x^{4} −14x^{3} − 59x^{2} − 57x −18
a. Possible Rational Zeros:
b. Descartes’ Rule of Signs :
f (−x) = x^{6} − 7x^{5} +12x^{4} + 14x^{3} −
59x^{2} + 57x −18
c. Synthetic Division :
d. x = 2, − 1,−1,−1,−3,−3
(2.) f ( x) = −4x^{3} + 15x^{2} − 8x − 3
a. Possible Rational Zeros:
b. Descartes’ Rule of Signs :
f (−x) = +4x^{3} + 15x^{2} + 8x − 3
c. Synthetic Division :
d. x = −1/4,1,3
(3.) f ( x) = x^{4} − 4x^{3} + 8x^{2} −16x + 16
a. Possible Rational Zeros:
b. Descartes’ Rule of Signs :
f (−x) = x^{4} + 4x^{3} + 8x^{2} + 16x + 16
c. Synthetic Division :
d. x = ± 2i, 2 ( multiplicity of 2)
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