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\(3x^4-4x^3+1\)
\(=3x^4+2x^3+x^2-6x^3-4x^2-2x+3x^2+2x+1\)
\(=x^2\left(3x^2+2x+1\right)-2x\left(3x^2+2x-1\right)+\left(3x^2+2x+1\right)\)
\(=\left(x^2-2x+1\right)\left(3x^2+2x+1\right)\)
\(=\left(3x^2+2x+1\right)\left(x-1\right)^2\)