Đáp án:
$\bullet$ `M (x) = x^2 + x^4 - 2x - 10`
`-> M (x) = x^4 + x^2 - 2x-10`
$\bullet$ `N (x) = 2x + 4x^4 - 2x^3 + 7`
`-> N (x) = 2x^4 - 2x^3 + 2x + 7`
`a,`
$\bullet$ `M (x) +N (x) = x^4 + x^2 - 2x-10 + 2x^4 - 2x^3 + 2x + 7`
`-> M (x) + N (x) = (x^4 + 2x^4) + x^2 + (-2x + 2x) + (-10 + 7) - 2x^3`
`-> M (x) + N (x) = 3x^4 + x^2 - 3 - 2x^3`
$\bullet$ `N (x) - M (x) = 2x^4 - 2x^3 + 2x + 7 - x^4 - x^2 + 2x + 10`
`-> N (x) - M (x) = (2x^4 - x^4) - 2x^3 + (2x + 2x) + (7 + 10) - x^2`
`-> N (x) - M (x) = x^4 - 2x^3 + 4x + 17 - x^2`
`b,`
`P (x) + x^2 - 1001 = M (x)`
`-> P (x) = M (x) - x^2+ 1001`
`-> P (x) = x^4 + x^2 - 2x-10 - x^2 + 1001`
`-> P (x) = x^4 + (x^2 - x^2) - 2x + (-10 + 1001)`
`-> P (x) = x^4 - 2x + 991`
Vậy `P (x) = x^4 - 2x + 991`
