Question

Is (x+1) a factor of f(x) = x^3 - 3x^2 + 4x + 8?

Option 1: Yes because the remainder is 0.
Option 2: No because the remainder is 0.
Option 3: No because the remainder is 8.
Option 4: No because the remainder is 10.

Answer 1

Yes, (x+1) is a factor of f(x) = x^3 - 3x^2 + 4x + 8.

Step-by-step explanation:

To determine if (x+1) is a factor of f(x) = x^3 - 3x^2 + 4x + 8, we need to check if the remainder when f(x) is divided by (x+1) is 0. We can use synthetic division to perform the division. The coefficients of f(x) are 1, -3, 4, and 8. Writing them in the synthetic division setup, we have:

-1 | 1 -3 4 8
| -1 4 -8
___________________________
1 -4 8 0

The last entry in the bottom row represents the remainder. Since the remainder is 0, (x+1) is a factor of f(x). Therefore, option 1: Yes because the remainder is 0 is the correct answer.