12) which of the following is factor of the polynomial x^4+x^3-x^2+x-1 x+1
x-1
Both options 1 and 2
None

None

Step-by-step explanation:

Polynomial Remainder Theorem

The polynomial remainder theorem establishes that the remainder of the division of a polynomial f(x) by (x-k) is equal to f(k), that is, substituting x for k.

We are given the polynomial:

And it's required to know if (x+1) and/or (x-1) are factors of the polynomial.

We apply the theorem for both cases.

For (x+1), we substitute x=-1 into the polynomial:

Since the remainder is not zero, x+1 is not a factor of the given polynomial.

For (x-1), we substitute x=1 into the polynomial:

Since the remainder is not zero, x-1 is not a factor of the given polynomial.

None

it should be a.

hope it

i believe b is the answer