a,\(x^2-x+2=x^2-2.\dfrac{1}{2}x+\dfrac{1}{4}+\dfrac{7}{4}\\ =\left(x-\dfrac{1}{2}\right)^2+\dfrac{7}{4}\)
\(b,x^2-2.\dfrac{1}{2}x+\dfrac{1}{4}+\dfrac{23}{4}\\ =\left(x-\dfrac{1}{2}\right)^2+\dfrac{23}{4}\)
\(x^2-x-2=\left(x-2\right)\left(x+1\right)\)
\(x^2-x-6=\left(x-3\right)\left(x+2\right)\)