\(d, x^3+4x^2-29x+24\)
\(=x^3+8x^2-4x^2-32x+3x+24\)
\(=x^2\left(x+8\right)-4x\left(x+8\right)+3\left(x+8\right)\)
\(=\left(x+8\right)\left(x^2-4x+3\right)\)
\(=\left(x+8\right)\left(x^2-x-3x+3\right)\)
\(=\left(x+8\right)\left[x\left(x-1\right)-3\left(x-1\right)\right]\)
\(=\left(x+8\right)\left(x-1\right)\left(x-3\right)\)
\(e, x^3+6x^2+11x+6\)
\(=x^3+3x^2+3x^2+9x+2x+3\)
\(=x^2\left(x+3\right)+3x\left(x+3\right)+2\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2+3x+2\right)\)
\(=\left(x+3\right)\left(x^2+x+2x+2\right)\)
\(=\left(x+3\right)\left[x\left(x+1\right)+2\left(x+1\right)\right]\)
\(=\left(x+3\right)\left(x+1\right)\left(x+2\right)\)
Mik ko giỏi p/t bậc 3 cho lắm nên có sai thì mong bạn sửa giúp :
d ) \(x^3+4x^2-29x+24\)
\(=x^2\left(x-1\right)+5x^2-10x+5-19x+19\)
\(=x^2\left(x-1\right)+5\left(x-1\right)^2-19\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+5x-5-19\right)\)
\(=\left(x-1\right)\left(x^2+5x-14\right)\)
\(=\left(x-1\right)\left(x^2+7x-2x-14\right)\)
\(=\left(x-1\right)\left(x+7\right)\left(x-2\right)\)
e ) \(x^3+6x^2+11x+6\)
\(=x^2\left(x+1\right)+5x^2+10x+5+x+1\)
\(=x^2\left(x+1\right)+5\left(x+1\right)^2+x+1\)
\(=\left(x+1\right)\left(x^2+5x+5+1\right)\)
\(=\left(x+1\right)\left(x^2+5x+6\right)\)
