\(\left(x^2+5x\right)^2-2\left(x^2+5x\right)-24\\ =\left[\left(x^2+5x\right)^2-6\left(x^2+5x\right)\right]+\left[4\left(x^2+5x\right)-24\right]\\ =\left(x^2+5x\right)\left(x^2+5x-6\right)+4\left(x^2+5x-6\right)\\ =\left(x^2+5x-6\right)\left(x^2+5x+4\right)\\ =\left(x^2-x+6x-6\right)\left(x^2+4x+x+4\right)\\ =\left[x\left(x-1\right)+6\left(x-1\right)\right]+\left[x\left(x+4\right)+\left(x+4\right)\right]\\ =\left(x-1\right)\left(x+1\right)\left(x+4\right)\left(x+6\right)\)

(x2+5x)2−2(x2+5x)−24=[(x2+5x)2−6(x2+5x)]+[4(x2+5x)−24]=(x2+5x)(x2+5x−6)+4(x2+5x−6)=(x2+5x−6)(x2+5x+4)=(x2−x+6x−6)(x2+4x+x+4)=[x(x−1)+6(x−1)]+[x(x+4)+(x+4)]=(x−1)(x+1)(x+4)(x+6)

đặt a=x^2-5x

(x^2-5x)^2+10(x^2-5x+24)

=a^2+10(a+24)

=a^2+10a+24

=a^2+6a+4a+24

=a(a+6)+4(a+6)

=(a+6)(a+4)

=(x^2-5x+6)(x^2-5x+4)

=[x^2-3x-2x+6][x^2-x-4x+4]

=[x(x-3)-2(x-3)][x(x-1)+4(x-1)]

=(x-3)(x-2)(x-1)(x+4)

\(x^3+5x^2+5x+1\)

\(=\left(x+1\right)\left(x^2+x+1\right)+5x\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2+6x+1\right)\)

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

\(=x^2+2\cdot\dfrac{5}{2}x+\dfrac{25}{4}-\dfrac{25}{4}-2\\ =\left(x+\dfrac{5}{2}\right)^2-\dfrac{33}{4}\\ =\left(x+\dfrac{5}{2}-\dfrac{\sqrt{33}}{2}\right)\left(x+\dfrac{5}{2}+\dfrac{\sqrt{33}}{2}\right)\)

\(A=5x^3-125x=5x\left(x-5\right)\left(x+5\right)\)

\(B=x^3-8+\left(x-2\right)\left(5x+4\right)\)

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

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

\(x^4-5x^2+4=\left(x^2-4\right)\left(x^2-1\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\)