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Đáp án $: A(x) = x^2 - 2x$

`B(x) = 8x^3 - 3x^2 + 6x + 10`

`c) x in {0 ; 2}`

Các bước giải 

`a) A(x) = P(x) + Q(x)`

`= ( 4x^3 - x^2 + 2x + 5 ) + ( -4x^3 + 2x^2 - 4x - 5 )`

`= 4x^3 - x^2 + 2x + 5 - 4x^3 + 2x^2 - 4x - 5`

`= ( 4x^3 - 4x^3 ) + ( 2x^2 - x^2 ) + ( 2x - 4x ) + ( 5 - 5 )`

`= x^2 - 2x`

`b) B(x) = P(x) - Q(x)`

`= ( 4x^3 - x^2 + 2x + 5 ) - ( -4x^3 + 2x^2 - 4x - 5 )`

`= 4x^3 - x^2 + 2x + 5 + 4x^3 - 2x^2 + 4x + 5`

`= ( 4x^3 + 4x^3 ) + ( -2x^2 - x^2 ) + ( 2x + 4x ) + ( 5 + 5 )`

`= 8x^3 - 3x^2 + 6x + 10`

`c) A(x) = x^2 - 2x`

`=> x . x - 2 . x`

`=> x . ( x - 2 )`

Cho `x . ( x - 2 ) = 0`

`=>` $\left[\begin{matrix} x=0\\ x-2=0\end{matrix}\right.$

`=>` $\left[\begin{matrix} x=0\\ x=0+2\end{matrix}\right.$

`=>` $\left[\begin{matrix} x=0\\ x=2\end{matrix}\right.$

Vậy `x in {0 ; 2}`