You have the following functions:
f(x) = 3x³ - 4x² + 5x - 18
g(x) = x - 2
in order to determine which statems area true, make the operations:
f(x) + g(x) = 3x³ - 4x² + 5x - 18 + x - 2 = 3x³ - 4x² + 6x - 20 FALSE
f(x) - g(x) = 3x³ - 4x² + 5x - 18 - (x - 2) = 3x³ - 4x² + 4x - 16 FALSE
f(x) x g(x) = (3x³ - 4x² + 5x - 18)(x - 2)
= 3x⁴ - 6x³ - 4x³ + 8x² + 5x² - 10x - 18x + 36
= 3x⁴ - 10x³ + 13x² - 28x + 36 FALSE
f(x)/g(x):
3x³ - 4x² + 5x - 18 | x - 2
-3x³ + 6x² 3x² + 2x + 9
2x² + 5x - 18
-2x² + 4x
9x - 18
-9x + 18
0
then:
f(x)/g(x) = 3x² + 2x + 9 x ≠ 2 TRUE