Answer:
3x³ - 7x² - x + 1
Step-by-step explanation:
For a function f(x) to have a remainder of -5 when divided by x - 2, f(2) must be equal to -5
For the function f(x) = 3x³ - 7x² - x + 1
Substitute x = 2 into the function
f(2) = 3(2)³ - 7(2)² - (2) + 1
f(2) = 3(8) - 7(4) - 2 + 1
f(2) = 24 - 28 - 2 + 1
f(2) = -5
Since the value of f(x) = 3x³ - 7x² - x + 1 is -5 for x = 2, then it has a remainder of -5 when divided by x - 2.
Other functions in the options do not give -5 as the result when x = 2 is substituted into them. Therefore, they do not have a remainder of -5 when divided by x - 2.