Cho các đa thức:  A(x) = 2x + {x^3} - 5{x^2} + 3;  B(x)= 2{x^2} + x + 1;   C(x) = 4 - 3x a) Tính A(x) + B(x), B(x) - C(x) b) Tính A(x) - B(x)+ C(x)

a)

\(\begin{array}{l}A\left( x \right) + B\left( x \right) = \left( {2x + {x^3} - 5{x^2} + 3} \right) + \left( {2{x^2} + x + 1} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {x^3} + \left( { - 5{x^2} + 2{x^2}} \right) + \left( {2x + x} \right) + \left( {3 + 1} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {x^3} - 3{x^2} + 3x + 4\end{array}\)

\(\begin{array}{l}B\left( x \right) - C\left( x \right) = \left( {2{x^2} + x + 1} \right) - \left( {4 - 3x} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2{x^2} + \left( {x + 3x} \right) + \left( {1 - 4} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2{x^2} + 4x - 3\end{array}\)

b)

\(\begin{array}{l}A\left( x \right) - B\left( x \right) + C\left( x \right) = \left( {2x + {x^3} - 5{x^2} + 3} \right) - \left( {2{x^2} + x + 1} \right) + \left( {4 - 3x} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {x^3} + \left( { - 5{x^2} - 2{x^2}} \right) + \left( {2x - x - 3x} \right) + \left( {3 - 1 + 4} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {x^3} - 7{x^2} - 2x + 6\end{array}\)

c)

          \(\begin{array}{l}D\left( x \right) = C\left( x \right) - A\left( x \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {4 - 3x} \right) - \left( {2x + {x^3} - 5{x^2} + 3} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - {x^3} + 5{x^2} + \left( { - 3x - 2x} \right) + \left( {4 - 3} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - {x^3} + 5{x^2} - 5x + 1\end{array}\)