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

Question

1-x²+x⁴ divided by x²+x+1 Find the quotient and remainder. Check your work by verifying that (quotient)(divisor)+(remainder) =dividend

Answer 1

By using long division.

 

quotient = x² - x - 1

divisor = x² + x + 1

remainder = 2x + 2

Multiply the quotient and divisor = x⁴ - x² - 2x - 1. Add this to the remainder to get x⁴ - x²  + 1