Question

What is the remainder when \(x^4 + x^3 - 2x^2 + x + 1\) is divided by \(x - 1\)?

a) 0
b) 1
c) 2
d) -1

Answer 1

The remainder when the polynomial x^4 + x^3 - 2x^2 + x + 1 is divided by x - 1 is calculated using the Remainder Theorem, and after substituting x with 1, the remainder is found to be 2.The correct option is C.

Step-by-step explanation:

To find the remainder when dividing the polynomial x4 + x3 - 2x2 + x + 1 by x - 1, we can apply the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) when divided by x - k is equal to f(k).

In this case, k is equal to 1, so we need to evaluate f(1). Substituting x with 1 in the given polynomial yields: 14 + 13 - 2(12) + 1 + 1 which simplifies to 1 + 1 - 2 + 1 + 1. Calculating this expression gives us 2, which is the remainder.

Therefore, the correct answer is (c) 2.