Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
x3−3x+1,x5−4x3+x2+3x+1
(2 marks)
x3−3x+1,x5−4x3+x2+3x+1
x2−1x3−3x+1x5−4x3+x2+3x+1x5−3x3+x2− + −¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ −x3+3x+1 −x3+3x−1––––––––––––––––––– 2
[1 mark]
Since the remainder ≠ 0,
x3−3x+1, couldn't exactly divide x5−4x3+x2+3x+1 as it leaves 2 as remainder. Hence, it not a factor of x5−4x3+x2+3x+1.
[1 mark]