Chapter A.3, Problem 69AYU

To determine

To find: The quotient and remainder.

Answer to Problem 69AYU

The quotient is $x^2-x-1$ and remainder is $2x+2$.

Explanation of Solution

Given:

$1-x^2+x^4$ divided by $x^2+x+1$.

Calculation:

$(\text{Quotient})(\text{Divisor})+\text{Remainder}=(x^2-x-1)(x^2+x+1)+(2x+2)$

$=x^4-x^3-x^2+x^3-x^2-x+x^2-x-1+2x+2$

$=x^4-x^2+1=\text{Dividend}$