\(a,3x^3-x^2-21x+7\)
\(=x^2\left(3x-1\right)-7\left(3x-1\right)\)
\(=\left(3x-1\right)\left(x^2-7\right)\)
\(b,x^3-4x^2+8x-8\)
\(=\left(x^3-8\right)-4x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+4\right)-4x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+4-4x\right)\)
\(=\left(x-2\right)\left(x^2-2x+4\right)\)
\(c,x^3-5x^2-5x+1\)
\(=\left(x^2+1\right)-5x\left(x+1\right)\)
=\(\left(x+1\right)\left(x^2-x+1\right)-5x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-5x\right)=\left(x+1\right)\left(x^2-4x+1\right)\)
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