b, \(x^2-6x-2=x^2-6x+9-11=\left(x-3\right)^2-\sqrt{11}^2\)
\(=\left(x-3-\sqrt{11}\right)\left(x-3+\sqrt{11}\right)\)
c,\(9x^2+6x-1=\left(3x\right)^2+2.3x+1-2=\left(3x+1\right)^2-\sqrt{2}^2\)
\(=\left(3x+1-\sqrt{2}\right)\left(3x+1+\sqrt{2}\right)\)
d,\(x^8+64=\left(x^4\right)^2+8^2+16x^4-16x^4\)
\(=\left(x^4+8\right)^2-\left(4x^2\right)^2=\left(x^4+4x^2+8\right)\left(x^4-4x^2+8\right)\)
e,\(81x^4+4=\left(9x^2\right)^2+2^2+36x^2-36x^2=\left(9x^2+2\right)^2-\left(6x\right)^2\)
\(=\left(9x^2+2-6x\right)\left(9x^2+6x+2\right)\)
g,\(x^8+x^7+1\)
\(=\left(x^8+x^7+x^6\right)+\left(x^5+x^4+x^3\right)+\left(x^2+x+1\right)-\left(x^6+x^5+x^4\right)-\left(x^3+x^2+x\right)\)
\(=x^6\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)+\left(x^2+x+1\right)-x^4\left(x^2+x+1\right)-x\left(x^2+x+1\right)\)\(\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)