`a) P(x) = 5x^3 - 3x + 7 - x`
` = 5x^3 - (3x+x) + 7`
` = 5x^3 - 4x + 7`
` Q(x) = -5x^3 + 2x - 3 + 2x - x^2 - 2`
` = -5x^3 -x^2 + (2x+2x) - (3+2)`
` = -5x^3 - x^2 + 4x - 5`
`b)`
`P(x) + Q(x) = (5x^3 - 4x + 7)+(-5x^3 - x^2 + 4x - 5)`
` = 5x^3 - 4x + 7 - 5x^3 -x^2 + 4x-5`
` = (5x^3-5x^3) -x^2+ (4x-4x) + (7-5)`
` = 2 -x^2`
Vậy `P(x) +Q(x) = 2-x^2`
`P(x) - Q(x) = (5x^3 - 4x + 7)-(-5x^3 - x^2 + 4x - 5)`
` = 5x^3 - 4x + 7 + 5x^3 +x^2 - 4x+5`
` = (5x^3+5x^3) +x^2+ (-4x-4x) + (7+5)`
` = 10x^3 + x^2 - 8x + 12`
Vậy `P(x) -Q(x) = 10x^3 + x^2 - 8x + 12`
`c)` Ta có :
`P(x) + Q(x) = 2-x^2`
Cho `2-x^2=0`
`=> x^2 = 2`
`=> x^2 = (\sqrt{2})^2`
`=> x\in{\sqrt{2}; -\sqrt{2}}`
Vậy đa thức `2-x^2` có nghiệm `x=\sqrt{2}` và `x=-sqrt{2}`
