Tính \(A\left( x \right) = M\left( x \right) + N\left( x \right)\) và \(B\left( x \right) = M\left( x \right) - N\left( x \right)\)

* Hướng dẫn giải

Ta có:

\(\begin{array}{l}M\left( x \right)\,\, = 5{x^4} - {x^3} + {x^2} + 5x - 5;\,\,N\left( x \right) = 5{x^4} - {x^3} - 4{x^2} + 6x - 5\\A\left( x \right)\,\,\,\, = M\left( x \right) + N\left( x \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = (5{x^4} - {x^3} + {x^2} + 5x - 5) + \left( {5{x^4} - {x^3} - 4{x^2} + 6x - 5} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {5{x^4} + 5{x^4}} \right) + \left( { - {x^3} - {x^3}} \right) + \left( {{x^2} - 4{x^2}} \right) + \left( {5x + 6x} \right) + \left( { - 5 - 5} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10{x^4} - 2{x^3} - 3{x^2} + 11x - 10\\B\left( x \right) = M\left( x \right) - N\left( x \right)\\ = (5{x^4} - {x^3} + {x^2} + 5x - 5) - \left( {5{x^4} - {x^3} - 4{x^2} + 6x - 5} \right)\\ = 5{x^4} - {x^3} + {x^2} + 5x - 5 - 5{x^4} + {x^3} + 4{x^2} - 6x + 5\\ = \left( {5{x^4} - 5{x^4}} \right) + \left( { - {x^3} + {x^3}} \right) + \left( {{x^2} + 4{x^2}} \right) + \left( {5x - 6x} \right) + \left( {5 - 5} \right)\\ = 5{x^2} - x\end{array}\)

Vậy \(A\left( x \right)\, = 10{x^4} - 2{x^3} - 3{x^2} + 11x - 10;\,B\left( x \right) = 5{x^2} - x\)

Chọn A