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vipboycodon

a) x8+x+1x^8+x+1
= x8−x2+x2+x+1x^8-x^2+x^2+x+1
= x2(x3+1)(x−1)(x2+x+1)+x2+x+1x^2(x^3+1)(x-1)(x^2+x+1)+x^2+x+1
= (x2+x+1)(x6−x5+x3−x2+1)(x^2+x+1)(x^6-x^5+x^3-x^2+1)

b) x8+x7+1=x8−x2+x7−x+x2+x+1x^8+x^7+1 = x^8-x^2+x^7-x+x^2+x+1
= x2(x3+1)(x−1)(x2+x+1)+x(x3+1)(x−1)(x2+x+1)+x2+x+1x^2(x^3+1)(x-1)(x^2+x+1)+x(x^3+1)(x-1)(x^2+x+1)+x^2+x+1
= (x2+x+1)(x6−x4+x3−x+1)(x^2+x+1)(x^6-x^4+x^3-x+1)
 
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