a.
\(=\left[\left(3x-1\right)^2\right]^2+2\left(3x-1\right)^2+1\)
\(=\left[\left(3x-1\right)^2+1\right]^2=\left(9x^2-6x+2\right)^2\)
b.
\(=2x^3-x^2+x-2x^2+x-1\)
\(=x\left(2x^2-x+1\right)-\left(2x^2-x+1\right)\)
\(=\left(x-1\right)\left(2x^2-x+1\right)\)
c.
\(=\left(x^5-x^4+x^2\right)+\left(x^4-x^3+x\right)+x^3-x^2+1\)
\(=x^2\left(x^3-x^2+1\right)+x\left(x^3-x^2+1\right)+x^3-x^2+1\)
\(=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
d.
\(=2x^4+10x^3+4x^2-6x+\left(2x^3+10x^2+4x-6\right)\)
\(=2x\left(x^3+5x^2+2x-3\right)+2\left(x^3+5x^2+2x-3\right)\)
\(=2\left(x+1\right)\left(x^3+5x^2+2x-3\right)\)