Question

x^7+x^2+1

Answer 1

\(x^7+x^2+1\)

\(=x^7+x^6+x^5-x^6-x^5-x^4+x^4+x^3+x^2-x^3-x^2-x+x^2+x+1\)

\(=x^5\left(x^2+x+1\right)-x^4\left(x^2+x+1\right)+x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^5-x^4+x^2-x+1\right)\left(x^2+x+1\right)\).

Answer 2

\(x^7+x^2+1\\ =x^7+x^2+1-x+x\\ =\left(x^7-x\right)+\left(x^2+x+1\right)\\ =x\left(x^6-1\right)+\left(x^2+x+1\right)\\ =x\left(x^3+1\right)\left(x^3-1\right)+\left(x^2+x+1\right)\\ =\left(x^4+x\right)\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\\ =\left(x^5-x^4+x^2-x\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^5-x^4+x^2-x+1\right)\)

Answer 3

\(x^7+x^2+1\\ =x^7+x^2+1+x-x\\ =\left(x^7-x\right)+\left(x^2+x+1\right)\\ =x\left(x^6-1\right)+\left(x^2+x+1\right)\\ =x\left(x^3+1\right)\left(x^3-1\right)+\left(x^2+x+1\right)\\ =\left(x^4+x\right)\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\\ =\left(x^5-x^4+x^2-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^5-x^4+x^2-1+1\right)\\ =\left(x^2+x+1\right)\left(x^5-x^4+x^2\right)\\ =\left(x^2+x+1\right)x^2\left(x^3-x^2+1\right)\)

Answer 4

Kỳ lạ

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