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)