a) \(3x^3-8x^2-41x+30\)

\(=\left(3x^3-15x^2\right)+\left(7x^2-35x\right)-\left(6x-30\right)\\ =3x^2\left(x-5\right)+7x\left(x-5\right)-6\left(x-5\right)\\ =\left(x-5\right)\left(3x^2+7x-6\right)\\ =\left(x-5\right)\left(3x^2+9x-2x-6\right)\\ =\left(x-5\right)\left[3x\left(x+3\right)-2\left(x+3\right)\right]\\ =\left(x-5\right)\left(x+3\right)\left(3x-2\right)\)

b) \(2x^2-3x-2\)

\(=2x^2-4x+x-2\\ =2x\left(x-2\right)+\left(x-2\right)\\ =\left(2x+1\right)\left(x-2\right)\)

c) \(x^3-8y^3-2xy\left(x-2y\right)\)

\(=\left(x-2y\right)\left(x^2+2xy+4y^2\right)-2xy\left(x-2y\right)\\ =\left(x-2y\right)\left(x^2+4y^2\right)\)

a) \(\left(x-\sqrt{y}\right)^3=x^3-3x^2\sqrt{y}+3xy-y\sqrt{y}\)

b) \(\left(x+2\right)^3-\left(x-2\right)^3-12x^3\)

\(=x^3+6x^2+12x+8-\left(x^3-6x^2+12x-8\right)-12x^3\\ =-12x^3+12x^2+16\)

\(x^2+5x+4=0\Rightarrow\left(x+4\right)\left(x+1\right)=0\Rightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)