`a) Q = – 2x^3 + 2x^2 + 12 + 5x^2 – 9x`
`= -2x^3 + (2x^2 + 5x^2) - 9x + 12`
`= -2x^3 + 7x^2 - 9x + 12`
`b) P = 4x^3 - 7x^2 + 3x - 12`
`⇒ 2P = 8x^3 - 14x^2 + 6x - 24`
`+) ⇒ P + Q = (4x^3 - 7x^2 + 3x - 12) + (-2x^3 + 7x^2 - 9x + 12)`
`= (4x^3 - 2x^3) + (-7x^2 + 7x^2) + (3x - 9x) + (-12 + 12)`
`= 2x^3 - 6x`
Vậy `P + Q = 2x^3 - 6x`
`+) 2P - Q = (8x^3 - 14x^2 + 6x - 24) - (-2x^3 + 7x^2 - 9x + 12)`
`= 8x^3 - 14x^2 + 6x - 24 + 2x^3 - 7x^2 + 9x - 12`
`= (8x^3 + 2x^3) - (14x^2 + 7x^2) + (6x + 9x) - (24 + 12)`
`= 10x^3 - 21x^2 + 15x - 36`
Vậy `2P - Q = 10x^3 - 21x^2 + 15x - 36`
`c) P + Q = 2x^3 - 6x`
Đặt `P + Q = 0 ⇒ 2x^3 - 6x = 0`
`⇒ 2. x. (x^2 - 3) = 0`
`⇒ x. (x^2 - 3) = 0`
`⇒` \(\left[ \begin{array}{l}x=0\\x^2-3=0\end{array} \right.\)
`⇒` \(\left[ \begin{array}{l}x=0\\x^2 = 3\end{array} \right.\)
`⇒` \(\left[ \begin{array}{l}x=0\\x= ±\sqrt{3}\end{array} \right.\)
Vậy `x = 0, x = \sqrt{3}, x = - \sqrt{3}` là nghiệm của `P + Q`.
