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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
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