\(x\left(x+4\right)\left(x+6\right)\left(x+10\right)+128\)
\(=\left(x^2+10x\right)\left(x^2+10x+24\right)+128\)
\(=\left(x^2+10x\right)^2+24\left(x^2+10x\right)+128\)
\(=\left(x^2+10x\right)^2+2\left(x^2+10x\right).12+144-16\)
\(=\left(x^2+10x\right)^2+2\left(x^2+10x\right).12+12^2-16\)
\(=\left(x^2+10x+12\right)^2-4^2\)
\(=\left(x^2+10x+12-4\right)\left(x^2+10x+12+4\right)\)
\(=\left(x^2+10x+8\right)\left(x^2+10x+16\right)\)
\(=\left(x^2+10x+8\right)\left(x^2+2x+8x+16\right)\)
\(=\left(x^2+10x+8\right)\left[x\left(x+2\right)+8\left(x+2\right)\right]\)
\(=\left(x^2+10x+8\right)\left(x+2\right)\left(x+8\right)\)
\(=\left(x^2+14x\right)\left(x^2+14x+48\right)+128\)
\(=\left(x^2+14x\right)^2+48\left(x^2+14x\right)+128\)
Đặt \(x^2+14x=a\)
\(A=a^2+48a+128=\left(a+24-8\sqrt{7}\right)\left(a+24+8\sqrt{7}\right)\)
\(=\left(x^2+14x+24-8\sqrt{7}\right)\left(x^2+14x+24+8\sqrt{7}\right)\)
