\(3x^4+2x^3-8x^2-2x+5\)
\(=3x^4-3x^3+5x^3-5x^2-3x^2+3x-5x+5\)
\(=3x^3\left(x-1\right)+5x^2\left(x-1\right)-3x\left(x-1\right)-5\left(x-1\right)\)
\(=\left(x-1\right)\left(3x^3+5x^2-3x-5\right)\)
\(=\left(x-1\right)\left[3x\left(x^2-1\right)+5\left(x^2-1\right)\right]\)
\(=\left(x-1\right)\left(3x+5\right)\left(x^2-1\right)\)
\(=\left(x-1\right)\left(3x+5\right)\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)^2\left(3x+5\right)\left(x-1\right)\)
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