Ta có : \(a^5+a+1\)
\(=\left(a^5-a^2\right)+\left(a^2+a+1\right)\)
\(=a^2\left(a^3-1\right)+\left(a^2+a+1\right)\)
\(=a^2\left(a-1\right)\left(a^2+a+1\right)+\left(a^2+a+1\right)\)
\(=\left(a^2+a+1\right)\left(a^3-a^2+1\right)\)
a5 + a + 1
= (a5 + a4 + a3) - (a4 + a3 + a2) + (a2 + a + 1)
= a3(a2 + a + 1) - a2(a2 + a + 1) + (a2 + a + 1)
= (a2 + a + 1)(a3 - a2 + 1)