a)\(x^2-8x+12=x^2-2x-6x+12=x\left(x-2\right)-6\left(x-2\right)=\left(x-6\right)\left(x-2\right)\)
b)\(x^2-4x-12=x^2+2x-6x-12=x\left(x+2\right)-6\left(x+2\right)=\left(x-6\right)\left(x+2\right)\)
c)\(\left(x^2+x\right)^2+4x^2+4x-12\)
\(=x^2\left(x+1\right)^2+4x\left(x+1\right)-12\)
\(=x\left(x+1\right)\left[x\left(x+1\right)+4\right]-12\)
\(=y\left(y+4\right)-12\) với \(y=x(x+1)\)
\(=y^2+4y-12\)
\(=y^2-2y+6y-12\)
\(=y\left(y-2\right)+6\left(y-2\right)\)
\(\left(y+6\right)\left(y-2\right)\)
nốt câu c=))
\(\left(x^2+x\right)^2+4x^2+4x-12=x^4+2x^3+x^2+4x^2+4x-12=x^4+2x^3+5x^2+10x-6x-12=x^3\left(x+2\right)+5x\left(x+2\right)-6\left(x+2\right)=\left(x+2\right)\left(x^3+5x-6\right)=\left(x+2\right)\left(x^3-x^2+x^2-x+6x-6\right)=\left(x+2\right)\left[x^2\left(x-1\right)+x\left(x-1\right)+6\left(x-1\right)\right]=\left(x+2\right)\left(x-1\right)\left(x^2+x+6\right)\)
