a) `x^2+7x+12=x^2+3x+4x+12=x(x+3)+4(x+3)=(x+3)(x+4)`
b) `a^10+a^5+1`
`=(a^5)^2 + 2.a^5 . 1/2 + (1/2)^2 + 3/4`
`=(a^5+1/2)^2+3/4`
`=>` Không thể phân tích thành nhân tử.
a) \(x^2+7x+12=\left(x+3\right)\left(x+4\right)\)
b) \(a^{10}+a^5+1=a^{10}-a+a^5-a^2+a^2+a+1\)
\(=a\left(a^9-1\right)+a^2\left(a-1\right)\left(a^2+a+1\right)+\left(a^2+a+1\right)\)
\(=a\left(a^3-1\right)\left(a^6+a^3+1\right)+\left(a^2+a+1\right)\left(a^3-a^2+1\right)\)
\(=a\left(a-1\right)\left(a^2+a+1\right)\left(a^6+a^3+1\right)+\left(a^2+a+1\right)\left(a^3-a^2+1\right)\)
\(=\left(a^2+a+1\right)\left[a\left(a-1\right)\left(a^6+a^3+1\right)+a^3-a^2+1\right]\)
