Question 2 (iii)
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
x5−4x3+x2+3x+1x5−3x3+x2− + −¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ −x3+3x+1 −x3+3x−1––––––––––––––––––– 2
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.