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Question Number 213123 by a.lgnaoui last updated on 30/Oct/24

factoriser x^5 +x^3 +x^2 −2x−1

factoriserx5+x3+x2−2x−1

Answered by MrGaster last updated on 30/Oct/24

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

(x5+x3+x2−2x−1)=(x−1)(x4+x3+2x2+3x+1)(x4+x3+2x2+3x+1)=(x+1)(x3+2x+1)(x3+2x+1)=(x+1)(x2−x+1)(x5+x3+x2−2x−1)=(x−1)(x+1)2(x2−x+1)

Commented by a.lgnaoui last updated on 30/Oct/24

thank you.

thankyou.

Commented by A5T last updated on 30/Oct/24

=x^5 −x+x^3 −x+x^2 −1 =x(x^2 −1)(x^2 +1)+x(x^2 −1)+x^2 −1 =(x−1)(x+1)(x^3 +2x+1) x^3 +2x+1≠(x+1)(x^2 −x+1)

=x5−x+x3−x+x2−1=x(x2−1)(x2+1)+x(x2−1)+x2−1=(x−1)(x+1)(x3+2x+1)x3+2x+1≠(x+1)(x2−x+1)

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