Answer:

True

Step-by-step explanation:

If the given statement is true. g(x) = (x/3) - (1/4) is a factor of f(x). And by remainder theorem when x = 3/4 [ x/3 - 1/4 1/3[ x - 3/4], numeric value of f(x) is 0.

Checking :

x = 3 / 4

f(x) = 8x³ - 6x² - 4x + 3

f(3/4) = 8(3/4)³ - 6(3/4)² - 4(3/4) + 3

= 8(27/64) - 6(9/16) - 3(1) + 3

= 27/8 - 27/8 - 3 + 3

= 0

As the result is 0, g(x) is a multiple of f(x).

Proved