\(\Leftrightarrow x^3-3x^2-3x^2+9x-10x+30\)

\(\Leftrightarrow x^2\left(x-3\right)-3x\left(x-3\right)-10\left(x-3\right)\)

\(\Leftrightarrow\left(x-3\right)\left(x^2-3x-10\right)\)

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

\(=\left(x^3-2x^2\right)+\left(8x^2-16x\right)+\left(15x-30\right)\)

\(=x^2\left(x-2\right)+8x\left(x-2\right)+15\left(x-2\right)\)

\(=\left(x-2\right)\left(x^2+8x+15\right)\)

\(=\left(x-2\right)\left(x^2+3x+5x+15\right)\)

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

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

Bài 1 :

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

Bài 2 :

 \(x^8+x^7+1=x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1-x^6-x^5-x^4-x^3-x^2-x\)

\(=x^6\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)+x^2+x+1-x^4\left(x^2+x+1\right)-x\left(x^2+x+1\right)\)

=\(\left(x^2+x+1\right)\left(x^6+x^3+1-x^4-x\right)\)

Tick đúng nha 

X^2-6+8

đặt y=x²+1

=>y²=(x²+1)²

y²=x⁴+2x²+1

đặt P(x)=x^4+6x^3+11x^2+6x+1

=x⁴+2x²+1+6x³+6x+9x²

=x⁴+2x+1+6x(x²+1)+9x²

thay y²=x⁴+2x²+1 và y=x²+1 ta được 

Q(y)=y²+6xy+9x²

=(y+3x)²

thay y=x²+1 ta được:

(x²+3x+1)²

vậy x^4+6x^3+11x^2+6x+1=(x²+3x+1)²

= (1 - x³ ) + ( 6x - 6x² ) 

= (1 - x ).(1 + x + x²) + 6x.(1 - x)

= (1 - x).(1+x+x² + 6x)

= (1 - x).(1 + 7x +x² )

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

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

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

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

x(2x^2-x-6)

x(2x^2-4x+3x-6)

x[2x(x-2)+3(x-2)]

x(2x+3)(x-2)

^{\(^{x^3-6x^2-x+30=x^3-5x^2-3x^2+15x-2x^2-10x-6x+30}\)}

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

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

=(x-5)[x(x-3)-2(x-3)]

=(x-5)(x-3)(x-2)

\(x^3-6x^2-x+30\) 

= \(x^3-5x^2-3x^2+15x+2x^2-10x-6x+30\)

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

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

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

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

a)\(=x^3+2x^2-8x^2-16x+15x+30\)

\(=x^2\left(x+2\right)-8x\left(x+2\right)+15\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2-8x+15\right)\)

\(=\left(x+2\right)\left(x^2-5x-3x+15\right)\)

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

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

nha