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Question Number 50924 by Saorey last updated on 22/Dec/18

factor the expression: E=x^5 +x^4 +1

factortheexpression:E=x5+x4+1

Answered by math1967 last updated on 22/Dec/18

x^5 −x^2 +x^4 +x^2 +1 =x^2 (x^3 −1)+{(x^2 +1)^2 −2x^2 +x^2 } =x^2 (x−1)(x^2 +x+1)+(x^2 +1)^2 −x^2 =x^2 (x−1)(x^2 +x+1)+(x^2 +x+1)(x^2 −x+1) =(x^2 +x+1)(x^3 −x^2 +x^2 −x+1) =(x^2 +x+1)(x^3 −x+1) ans

x5−x2+x4+x2+1=x2(x3−1)+{(x2+1)2−2x2+x2}=x2(x−1)(x2+x+1)+(x2+1)2−x2=x2(x−1)(x2+x+1)+(x2+x+1)(x2−x+1)=(x2+x+1)(x3−x2+x2−x+1)=(x2+x+1)(x3−x+1)ans

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