Verified answer

_____5x^2_______________

x^2+2|5x^4 +0x^3 -3x^2 +0x +4

...-.......5x^4...........+10x^2

...............0..+0x^3.-13x^2+0x+4

_____5x^2______-13_______

x^2+2|5x^4 +0x^3 -3x^2 +0x +4

...-.......5x^4...........+10x^2

...............0..+0x^3.-13x^2+0x+4

...-..........................-13x^2.......-26

.....................................0.........+30

SO our answer is 5x^2 -13 + (30/(x^2+2))

5x^2 - 13 remainder 30

ans is 5x^2-7 and remainder18

Explanation

5x^2-7

(x² + 2)|-------------------------

| 5x⁴ +0x^3- 3x² + 4

5x⁴ +0x^3+10x²

--------------------------------

-7x²+4

-7x²-14

------------------------

18

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