Question

BY actual division , find the quotient and the remainder when the first polynomial is divided by the second polynomial `x^(4)+1 and x-1` .

Answer 1

Using long method
`x-1)x^(4)+1(x^(3)+x^(2)+x+1`
`(x^(4)-x^(3))/(x^(3)+1)`
`(underline(x)^(3)underset(+)(-)x^(2))/(x^(2)+1)`
`(underline(x)^(2)underset(+)(-)x)/(x+1)`
`(underline(x)- underset(+)1)/(2)`
Hence ,Quotient `=x^(3)+x^(2)+x+1 ` and Remainder =2