Question

Is(x−1) a factor of f(x)=x⁴−2x²−x+2?

a) Yes
b) No
c) Yes, with a remainder of 1
d) No, with a remainder of 1

Answer 1

(x-1) is a factor of f(x)=x⁴-2x²-x+2.

Step-by-step explanation:

To determine if (x-1) is a factor of f(x)=x⁴-2x²-x+2, we can use synthetic division.

1. Set up the synthetic division table with the coefficients of f(x) and test the factor (x-1).
2. Perform the synthetic division by dividing each coefficient of f(x) by 1 (the value of x in (x-1)).
3. If the remainder is 0, then (x-1) is a factor of f(x). Otherwise, it is not.

Example:

Using synthetic division:

(x-1) | 1 -2 -1 2 | 1 -1 0

Since the remainder is 0, we can conclude that (x-1) is a factor of f(x).