Cho 2 đa thức M(x) = x² + x⁴ – 2x – 10 N(x) = 2x + 4x⁴ – 2x³ + 7 a) Tính M(x) + N(x) và N(x) – M(x) b) Tìm đa thức P(x) biết P(x) + x² – 1001 = M(x)

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`