a) \(x^2+7x+12\)
\(=\left(x^2+3x\right)+\left(4x+12\right)\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
b) \(x^2+6x+8\)
\(=\left(x^2+2x\right)+\left(4x+8\right)\)
\(=x\left(x+2\right)+4\left(x+2\right)\)
\(=\left(x+2\right)\left(x+4\right)\)
c) \(x^2-10x+16\)
\(=\left(x^2-2x\right)-\left(8x-16\right)\)
\(=x\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x-2\right)\left(x-8\right)\)
d) \(x^2-8x+15\)
\(=\left(x^2-3x\right)-\left(5x-15\right)\)
\(=x\left(x-3\right)-5\left(x-3\right)\)
\(=\left(x-3\right)\left(x-5\right)\)
e) \(x^2-8x-9\)
\(=\left(x^2+x\right)-\left(9x-9\right)\)
\(=x\left(x+1\right)-9\left(x+1\right)\)
\(=\left(x+1\right)\left(x-9\right)\)
f) \(x^2+14x+48\)
\(=\left(x^2+6x\right)+\left(8x+48\right)\)
\(=x\left(x+6\right)+8\left(x+6\right)\)
\(=\left(x+6\right)\left(x+8\right)\)
