\(b,=x^4-2x^3-x^3+2x^2+3x^2-6x-3x+6\\ =\left(x-2\right)\left(x^3-x^2+3x-3\right)\\ =\left(x-2\right)\left(x-1\right)\left(x^2+3\right)\\ c,=x^4-2x^3+4x^3-8x^2+4x^2-8x+3x-6\\ =\left(x-2\right)\left(x^3+4x^2+4x+3\right)\\ =\left(x-2\right)\left(x^3+3x^2+x^2+3x+x+3\right)\\ =\left(x-2\right)\left(x+3\right)\left(x^2+x+1\right)\)

\(x^3-x^2-14x+24\)

\(=x^3+4x^2-5x^2-20x+6x+24\)

\(=\left(x^3+4x^2\right)-\left(5x^2+20x\right)+\left(6x+24\right)\)

\(=x^2\left(x+4\right)-5x\left(x+4\right)+6\left(x+4\right)\)

\(=\left(x^2-5x+6\right)\left(x+4\right)\)

\(=\left(x^2-2x-3x+6\right)\left(x+4\right)\)

\(=\left[x\left(x-2\right)-3\left(x-2\right)\right]\left(x+4\right)\)

\(=\left(x-2\right)\left(x-3\right)\left(x+4\right)\)

\(x^4-x^2+2x+2\)

\(=x^4-2x^3+2x^2+2x^3-4x^2+4x+x^2-2x+2\)

\(=\left(x^4-2x^3+2x^2\right)+\left(2x^3-4x^2+4x\right)+\left(x^2-2x+2\right)\)

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

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

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

\(x^4-x^2+2x+2\)

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

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

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

\(=\left(x+1\right)\left(x^3-x^2+2\right)\)

Đa thức này ko phân tích thành nhân tử được

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

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

\(\dfrac{1}{4}x^2+2xy+4y^2=\left(\dfrac{1}{2}x+2y\right)^2\)