\(6x^2+7x-5=6x^2-3x+10x-5=3x\left(2x-1\right)+5\left(2x-1\right)\)
\(=\left(3x+5\right)\left(2x-1\right)\)
\(10x^2+17x+3=10x^2+2x+15x+3=2x\left(5x+1\right)+3\left(5x+1\right)\)
\(=\left(5x+1\right)\left(2x+3\right)\)
\(x-\sqrt{x}-2=x+\sqrt{x}-2\sqrt{x}-2=\sqrt{x}\left(\sqrt{x}+1\right)-2\left(\sqrt{x}+1\right)\)
\(=\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)\)
\(x+5\sqrt{x}+6=x+3\sqrt{x}+2\sqrt{x}+6=\sqrt{x}\left(\sqrt{x}+3\right)+2\left(\sqrt{x}+3\right)\)
\(=\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)\)