a, \(x^2+7x+12\)
\(=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)=\left(x+4\right)\left(x+4\right)\)
b, \(x^2-x-6\)
\(=x^2-3x+2x-6\)
\(=x\left(x-3\right)+2\left(x-3\right)=\left(x+2\right)\left(x-3\right)\)
c, \(2x^2+3x-2\)
\(=2x^2+4x-x-2\)
\(=2x\left(x+2\right)-\left(x+2\right)=\left(2x-1\right)\left(x+2\right)\)
d, \(x^3-7x-6\)
\(=x^3+2x^2-2x^2-4x-3x-6\)
\(=x^2\left(x+2\right)-2x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x^2-2x-3\right)\left(x+2\right)\)
\(=\left(x^2-3x+x-3\right)\left(x+2\right)\)
\(=\left[x\left(x-3\right)+\left(x-3\right)\right]\left(x+2\right)\)
\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\)
a) \(x^2+7x+12=x^2+4x+3x+12=x\left(x+4\right)+3\left(x+4\right)\\ =\left(x+4\right)\left(x+3\right)\)
b) \(x^2-x-6=x^2-3x+2x-6=x\left(x-3\right)+2\left(x-3\right)\\ =\left(x-3\right)\left(x+2\right)\)
c) \(2x^2+3x-2=2x^2+4x-x-2=2x\left(x+2\right)-\left(x+2\right)\\ =\left(x+2\right)\left(2x-1\right)\)
d) \(x^3-7x-6=x^3+2x^2-2x^2-4x-3x-6\\ =x^2\left(x+2\right)-2x\left(x+2\right)-3\left(x+2\right)\\ =\left(x+2\right)\left(x^2-2x-3\right)\\ =\left(x+2\right)\left(x^2+x-3x-3\right)\\ =\left(x+2\right)\left(x\left(x+1\right)-3\left(x+1\right)\right)\\ =\left(x+2\right)\left(x+1\right)\left(x-3\right)\)
