\(2x^3-5x-6\)

\(=2x^3-4x^2+4x^2-8x+3x-6\)

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

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

#\(Toru\)

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

(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)

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

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

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

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

#)Giải :

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

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

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

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

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

\(x^4+2x^3+5x^2+4x-12\)

\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)

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

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

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

Câu 1.

Đoán được nghiệm là 2.Ta giải như sau:

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

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

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

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

cảm ơn nha!

\(=\left(x+2\right)\left(5x-3-2x\right)\)

\(=x^2-5x+\dfrac{25}{4}-\dfrac{29}{4}\)

\(=\left(x-\dfrac{5}{2}\right)^2-\dfrac{29}{4}\)

\(=\left(x-\dfrac{5}{2}-\dfrac{\sqrt{29}}{2}\right)\left(x-\dfrac{5}{2}+\dfrac{\sqrt{29}}{2}\right)\)

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

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

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

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