1) \(x^3+6x^2+11x+6\)
\(=x^3+x^2+5x^2+5x+6x+6\)
\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x+1\right)\left(x^2+2x+3x+6\right)\)
\(=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
2) \(A=n^3\left(n^2-7\right)^2-36n\)
\(A=n\left[n^2\left(n^2-7\right)^2-36\right]\)
\(A=n\left\{\left[n\left(n^2-7\right)\right]^2-6^2\right\}\)
\(A=n\left(n^3-7n-6\right)\left(n^3-7n+6\right)\)
\(A=n\left(n^3-7n-6\right)\left(n^3-n-6n+6\right)\)
\(A=n\left(n^3-7n-6\right)\left[n\left(n-1\right)\left(n+1\right)-6\left(n-1\right)\right]\)
\(A=n\left(n^3-7n-6\right)\left(n-1\right)\left(n^2+n-6\right)\)
\(A=n\left(n-1\right)\left(n^3-7n-6\right)\left(n^2+3n-2n-6\right)\)
\(A=n\left(n-1\right)\left(n^3-7n-6\right)\left[n\left(n+3\right)-2\left(n+3\right)\right]\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n^3-7n-6\right)\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n^3-n-6n-6\right)\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left[n\left(n-1\right)\left(n+1\right)-6\left(n+1\right)\right]\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n+1\right)\left(n^2+n-6\right)\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n+1\right)\left(n^2+3n-2n-6\right)\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n+1\right)\left[n\left(n+3\right)-2\left(n+3\right)\right]\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n+1\right)\left(n+3\right)\left(n-2\right)\)
\(A=\left(n-1\right)n\left(n+1\right)\left(n-2\right)^2\left(n+3\right)^2\)
Rồi sao nữa còn nghĩ :))
