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Question

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
(2 marks)


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Solution

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

x21x33x+1x54x3+x2+3x+1x53x3+x2 + ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ x3+3x+1 x3+3x1––––––––––––––––– 2
[1 mark]

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.
[1 mark]


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