Question

Find the remainder when f(x)=32x^5-1 is divided by 4x^2-1

Answer 1

remainder will be 8x^3-1

Answer 2

' 8x^3 + 2x
-----------___________
4x^2--1 ) 32x^5 -- 1
' -- (32x^5 -- 8x^3)
' ----------------------
' 0 + 8x^3 -- 1
' -- (8x^3 --2x)
' ____________
= (0 + 2x -- 1 )

so remainder is 2x -- 1