Examples Illustrating the Functional Notation

Letf(x) = 2x³ - 3x² -23x +12
 f(4) = 2(4)³ - 3(4)² - 23(4) +12
 f(4) = 128 - 48 - 92 + 12
 f(4) = 0 
 The remainder when f(x) is divided by
x - 4 is 0
 ∴ x-4 is a factor of f(x)
 f(3) = 2(3)³ -3(3)² -23(3) +12
 f(3) = 54 - 27 -69 +12
 f(3) = -30
 The remainder when f(x) is divided by
x - 3 is -30