Question

Is (x + 3) a factor of f(x) = 4x3 + 11x2 − 75x + 18?

Answer 1

Answer:

No; the remainder is 0 so (x + 3) is not a factor

Step-by-step explanation:

Answer 2

Answer: B) No; the remainder is 234, so (x+3) is not a factor.

===============================================================

Explanation:

We'll use the remainder theorem. That theorem says if we divide p(x) over (x-k), then the remainder is p(k). A special case of this theorem says that if we get 0 as the remainder, then (x-k) is a factor of p(x).

We're dividing f(x) over (x+3) which means that k = -3. Think of x+3 as x-(-3) so you can match it up with the form x-k.

To find the remainder of f(x)/(x+3), we need to compute f(-3).

Plug x = -3 into the f(x) function to get...

f(x) = 4x^3 + 11x^2 - 75x + 18

f(-3) = 4(-3)^3 + 11(-3)^2 - 75(-3) + 18

f(-3) = 234

The remainder is 234, which is isn't zero, so (x+3) is not a factor of f(x).