Разложить на множители x^5+x^4+1, a^5+a+1

1.

x⁵+x+1=

=x⁵+x⁴-х⁴+x³-x³+x²-x²+x+1=

= (x⁵+x⁴+x³) - (x⁴+x³+x²) + (x²+x+1) =

=x³ (x²+x+1) - x² (x²+x+1) + (x²+x+1) =

= (x²+x+1) (x³-x²+1)

2.

a⁵+a+1=

= а⁵+а⁴-а⁴+а³-а³+а²-а²+а+1=

= (a⁵+a⁴+a³) - (a⁴+a³+a²) + (a²+a+1) =

=a³ (a²+a+1) - a² (a²+a+1) + (a²+a+1) =

= (a ² + a+1) (a ³ - a ² + 1)