Question

What is the remainder when P(x) = x ¹²³ + x ⁵⁶ + 1 is divided by x-1.

Answer 1

In order to calculate the remainder of this division, we can use the remainder theorem.

This theorem states that when dividing p(x) by q(x), and q(x) has a zero x = k, the remainder of the division is given by r = p(k).

Since the division is by the polynomial x - 1 and its zero is x = 1, let's calculate the value of p(1), which will be the remainder of the division:

`\begin{gathered} p(1)=1^(123)+1^(56)+1 \\ p(1)=1+1+1 \\ p(1)=3 \end{gathered}`

Therefore the remainder of the division is 3.