P(x)=x^4-2x^3+kx-4 where kis an unknown integer. P(x) divided by (x-1) has a remainder of 0. What is the value of k? k=square

To find the value of such that \( P(x) = x^4 - 2x^3 + kx - 4 \) has a remainder of 0 when divided by \( (x-1) \), we can use the Remainder Theorem. According to the Remainder Theorem, if a polynomial \( P(x) \) is divided by \( (x-a) \), the remainder is \( P(a) \).In this case, we are dividing \( P(x) \) by \( (x-1) \), so we need to evaluate \( P(1) \) and set it equal to 0. Since the remainder is 0, we have: Solving for , we get: Therefore, the value of is .