a/ \(6x^3-17x^2+14x-3\)
\(=6x^3-6x^2-11x^2+11x+3x-3\)
\(=6x^2\left(x-1\right)-11x\left(x-1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(6x^2-11x+3\right)\)
\(=\left(x-1\right)\left(6x^2-2x-9x+3\right)\)
\(=\left(x-1\right)\left[2x\left(3x-1\right)-3\left(3x-1\right)\right]\)
\(=\left(x-1\right)\left(2x-3\right)\left(3x-1\right)\)
b/ \(x^3-19x-30\)
\(=x^3+3x^2-3x^2-9x-10x-30\)
\(=x^2\left(x+3\right)-3x\left(x+3\right)-10\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x-10\right)\)
\(=\left(x+3\right)\left(x^2+2x-5x-10\right)\)
\(=\left(x+3\right)\left(x+2\right)\left(x-5\right)\)
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