a) nhận xét hệ số : 1 + 4 - 29 + 24 = 0

=> x³ + 4x² - 29x + 24 = x²(x-1) + 5x(x-1) - 24(x-1)

= (x-1)(x²+5x-24) = (x-1)(x-3)(x+8)

b) ...

a) \(x^3+4x^2-29x+24\)=\(\left(x+8\right)\left(x^2-4x+3\right)\)=\(\left(x+8\right)\left(x^2-x-3x+3\right)\)=\(\left(x+8\right)\left(x-1\right)\left(x-3\right)\)

b) \(x^4+6x^3+7x^2-6x+1\)=\(x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)=\(x^2\left(x^2+3x-1\right)+3x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)\)=\(\left(x^2+3x-1\right)\left(x^2+3x-1\right)\)=\(\left(x^2+3x-1\right)^2\)

\((x-1)(x-3)(x+8)\)

\(x^3+4x^2-29x+24\)

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

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

\(=\left(x+8\right)\left[x\left(x-1\right)-3\left(x-1\right)\right]\)

\(=\left(x+8\right)\left(x-1\right)\left(x-3\right)\)

= -2 ( x² + 2x + 1 ) + 32

= -2 ( x +1 )² + 32

= - 2 [ (x + 1 )² - 16 ]

= -2 [ (x + 1 ) ² - 4² ]

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

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

\(-2x^2-4x+30\)

\(=-2\left(x^2+2x+1\right)+32\)

\(=-2\left(x+1\right)^2+32\)

\(=-2\left[\left(x+1\right)^2-16\right]\)

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

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

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

a,   \(x^3+4x^2-29x+24\)

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

\(=x^2\left(x-1\right)+5x\left(x-1\right)-24\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+5x-24\right)\)

\(=\left(x-1\right)\left[x\left(x-3\right)+8\left(x-3\right)\right]\)

\(=\left(x-1\right)\left(x-3\right)\left(x+8\right)\)

      \(x^3+6x^2+11x+6\)

\(=x^3+x^2+5x^2+5x+6x+6\)

\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2+5x+6\right)\)

\(=\left(x+1\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)

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

Chúc bạn học tốt.

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

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

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

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

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

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

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

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

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

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

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

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

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

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