Considera os seguintes polinómios

Considera os seguintes polinómios.

\(A = 2{x^2} – x – 1\)        \(B = – 3{x^2} + 3x\)        \(C = 4{x^3} – 3\)       \(D = 2x + 6\)

1. O polinómio A tem grau 2.
   O polinómio B tem grau 2.
   O polinómio C tem grau 3.
   O polinómio D tem grau 1.
   
   
2. Em cada caso, na forma reduzida, o polinómio obtido é:

1. 
   \[\begin{array}{*{20}{l}}{A + B}& = &{\left( {2{x^2} – x – 1} \right) + \left( { – 3{x^2} + 3x} \right)}\\{}& = &{2{x^2} – x – 1 – 3{x^2} + 3x}\\{}& = &{ – {x^2} + 2x – 1}\end{array}\]
2. 
   \[\begin{array}{*{20}{l}}{A + C + D}& = &{\left( {2{x^2} – x – 1} \right) + \left( {4{x^3} – 3} \right) + \left( {2x + 6} \right)}\\{}& = &{2{x^2} – x – 1 + 4{x^3} – 3 + 2x + 6}\\{}& = &{4{x^3} + 2{x^2} + x + 2}\end{array}\]
3. 
   \[\begin{array}{*{20}{l}}{2B – 3D}& = &{2\left( { – 3{x^2} + 3x} \right) – 3\left( {2x + 6} \right)}\\{}& = &{ – 6{x^2} + 6x – 6x – 18}\\{}& = &{ – 6{x^2} – 18}\end{array}\]
4. 
   \[\begin{array}{*{20}{l}}{C \times D}& = &{\left( {4{x^3} – 3} \right) \times \left( {2x + 6} \right)}\\{}& = &{8{x^4} + 24{x^3} – 6x – 18}\end{array}\]