1) \(x^2+x-6\)

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

\(=\left(x^2-2x\right)+\left(3x-6\right)\)

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

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

2) \(x^2-x-6\)

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

\(=\left(x^2+2x\right)-\left(3x+6\right)\)

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

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

3) \(x^2+2x-48\)

\(=x^2+8x-6x-48\)

\(=\left(x^2+8x\right)-\left(6x+48\right)\)

\(=x\left(x+8\right)-6\left(x+8\right)\)

\(=\left(x+8\right)\left(x-6\right)\)

4) \(x^2-2x-48\)

\(=x^2-8x+6x-48\)

\(=\left(x^2-8x\right)+\left(6x-48\right)\)

​\(=x\left(x-8\right)+6\left(x-8\right)\)​

\(=\left(x-8\right)\left(x+6\right)\)

5) \(x^2+x-42\)

\(=x^2+7x-6x-42\)

\(=\left(x^2+7x\right)-\left(6x+42\right)\)

\(=x\left(x+7\right)-6\left(x+7\right)\)

\(=\left(x+7\right)\left(x-6\right)\)

6) \(x^2-x-42\)

\(=x^2-7x+6x-42\)

\(=\left(x^2-7x\right)+\left(6x-42\right)\)

\(=x\left(x-7\right)+6\left(x-7\right)\)

\(=\left(x-7\right)\left(x+6\right)\)