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\(x^{16}+x^8-2=x^{16}-x^8+2x^8-2=x^8\left(x^8-1\right)+2\left(x^8-1\right)\)
\(=\left(x^8+2\right)\left(x^8-1\right)=\left(x^8+2\right)\left(x^4+1\right)\left(x^4-1\right)\)
\(=\left(x^8+2\right)\left(x^4+1\right)\left(x^2+1\right)\left(x^2-1\right)\)
\(=\left(x^8+2\right)\left(x^4+1\right)\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\)
\(x^3+x^2+2x+8\)
\(=x^3+2x^2-x^2-2x+4x+8\)
\(=x^2\left(x+2\right)-x\left(x+2\right)+4\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-x+4\right)\)
(x2-8)2+36=x4-16x2+100=x4+20x2+100-36x2=(x2+10)2-36x2=(x2+10-6x)(x2+10+6x)
\(\left(x+2\right)\left(x+3\right)\left(x+8\right)\left(x+12\right)-4x^2\)
\(=\left(x+2\right)\left(x+12\right)\left(x+3\right)\left(x+8\right)-4x^2\)
\(=\left(x^2+14x+24\right)\left(x^2+11x+24\right)-\left(2x\right)^2\)
Đặt \(x^2+11x+24=a\)
\(=a\left(a+3x\right)-4x^2=a^2+3ax-4x^2=a^2-ax+4ax-4x^2=\left(a-x\right)\left(a+4x\right)\)
x2 + 2x - 4x - 8 = x(x+2) -4(x+2)
=(x-4)(x+2)