Question

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

Answer 1

Answer:

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

Answer 2

The answer to the question "Use the remainder theorem to determine whether x - 2 is a factor of $f(x) = x^3+3x^2-x-18$" is option A: Yes, x - 2 is a factor of f(x) because f(2) = 0

The given function is:

$f(x) = x^3+3x^2-x-18$

The function $f(x) = x^3+3x^2-x-18$ is divided by x - 2

x - 2 will be a factor of $f(x) = x^3+3x^2-x-18$ only if f(2) = 0

Substitute x = 2 into $f(x) = x^3+3x^2-x-18$

$f(2) = 2^3 + 3(2)^2 - 2 - 18\\\\f(2) = 8 + 3(4) - 2 - 18\\\\f(2) = 8 + 12 - 20\\\\f(2) = 20 - 20\\\\f(2) = 0$

Since f(2) = 0, then we  can conclude that x - 2 is a factor of  $f(x) = x^3+3x^2-x-18$

Learn more here: https://brainly.com/question/22237647