$$\eqalign{
& a)\,\,2{x^3} - 3{x^2} + x + a \cr
& \,\,\, = {x^2}\left( {2x - 3} \right) + x + a \cr
& Chia\,\,het\,\,cho\,\,x + a \cr
& \Rightarrow 2x - 3\,\,chia\,\,het\,\,cho\,\,x + a \cr
& \Leftrightarrow a = - {3 \over 2} \cr
& Bai5:\, \cr
& a)\,\,x - {x^2} - 1 \cr
& = - \left( {{x^2} - x} \right) - 1 \cr
& = - \left( {{x^2} - 2.x.{1 \over 2} + {1 \over 4}} \right) + {1 \over 4} - 1 \cr
& = - {\left( {x - {1 \over 2}} \right)^2} - {3 \over 4} < 0\,\,\forall x \in R \cr
& b)\,\,f\left( x \right) = {x^2} - 4x + 9 \cr
& f\left( x \right) = {x^2} - 4x + 4 + 5 \cr
& f\left( x \right) = {\left( {x - 2} \right)^2} + 5 \cr
& \Rightarrow f{\left( x \right)_{\min }} = 5 \Leftrightarrow x = 2 \cr} $$
