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\(2x^4-3x^3-14x^2-x+10\)
\(=\left(2x^4-4x^3-10x^2\right)+\left(x^3-2x^2-5x\right)-2x^2+4x+10\)
\(=2x^2\left(x^2-2x-5\right)+x\left(x^2-2x-5\right)-2\left(x^2-2x-5\right)\)
\(=\left(x^2-2x-5\right)\left(2x^2+x-2\right)\)
\(2x^2-3x\sqrt{x+3}+\left(x+3\right)\)
\(=2x^2-2x\sqrt{x+3}-x\sqrt{x+3}+\left(\sqrt{x+3}\right)^2\)
\(=2x\left(x-\sqrt{x+3}\right)-\sqrt{x+3}\left(x-\sqrt{x+3}\right)\)
\(=\left(2x-\sqrt{x+3}\right)\left(x-\sqrt{x+3}\right)\)
\(2x^2-3x\sqrt{x+3}+\left(x+3\right)\)
\(=2x^2-x\sqrt{x+3}-2x\sqrt{x+3}+\left(\sqrt{x+3}\right)^2\)
\(=x\left(2x-\sqrt{x+3}\right)-\sqrt{x+3}\left(2x-\sqrt{x+3}\right)\)
\(=\left(x-\sqrt{x+3}\right)\left(2x-\sqrt{x+3}\right)\)
\(C=x^2\left(x^2+x+1\right)-2x\left(x^2+x+1\right)+3\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-2x+3\right)\)
\(2x^4-3x^3-14x^2-x+10\)
\(=\left(2x^4+x^3-2x^2\right)+\left(-4x^3-2x^2+4x\right)+\left(-10x^2-5x+10\right)\)
\(=\left(2x^2+x-2\right)\left(x^2-2x-5\right)\)