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Question 2 (iii)
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

x33x+1,x54x3+x2+3x+1


Solution

x33x+1,x54x3+x2+3x+1

x21x33x+1x54x3+x2+3x+1x53x3+x2  +     ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯    x3+3x+1     x3+3x1–––––––––––––––––                2
Since the remainder 0,

x33x+1, couldn't exactly divide  x54x3+x2+3x+1 as it  leaves 2 as remainder. Hence, it not a factor of x54x3+x2+3x+1.

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