Use the remainder theorem to determine whether x - 2 is a factor of

f(x) = x3 + 3x2 - x - 18

A)

Yes, x - 2 is a factor of f(x) because f(2) = 0

B)

No, x - 2 is not a factor of f(x) because f(2) = 0

C)

Yes, x - 2 is a factor of f(x) because f(-2) = -12

D)

No, x - 2 is not a factor of f(x) because f(-2) = -12

The answer to the question "Use the remainder theorem to determine whether x - 2 is a factor of " is option A: Yes, x - 2 is a factor of f(x) because f(2) = 0

The given function is:

The function is divided by x - 2

x - 2 will be a factor of only if f(2) = 0

Substitute x = 2 into

Since f(2) = 0, then we  can conclude that x - 2 is a factor of  

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A

Step-by-step explanation:

To determine if (x - 2) is a factor of f(x)

Evaluate f(2) and if equal to zero then (x - 2) is a factor

f(2) = 2³ + 3(2)² - 2 - 18

     = 8 + 12 - 2 - 18

     = 0

(x - 2) is a factor of f(x) because f(2) = 0 → A