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Question Number 137335 by liberty last updated on 01/Apr/21

P(x) = 3x^75 + 2x^14 - 3x^2 - 1. What is the remainder when the above polynomial of s divided by x^2+x+1?\n

Answered by EDWIN88 last updated on 01/Apr/21

Apply the Factor theorem . That means to write x^2 = −x−1 and observe that x^3 =−x^2 −x=x+1−x=1 x^4 = x ; x^5 = −x−1 , x^6 = 1, x^7 =x it follows that 3x^(75) +2x^(14) −3x^2 −3 = 3(1)+2(x^2 )−3x^2 −1 = 2−x^2 =2−(−x−1)= x+3

ApplytheFactortheorem.Thatmeans towritex2=−x−1andobservethat x3=−x2−x=x+1−x=1 x4=x;x5=−x−1,x6=1,x7=x itfollowsthat Extra close brace or missing open brace Extra close brace or missing open brace

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