Divide the following rational function into the form of g(x)+((ax+b)/(x^2+4))?

Question

(x^5+6x^3+11x+7)

/(

x^2+4)

Answer 1

..................x³ + 2x

.................________________________

x² + 0x + 4) x⁵ + 0x⁴ + 6x³ + 0x² + 11x + 7 

...................x⁵ + 0x⁴ + 4x³

...................................2x³ + 0x² + 11x + 7 

...................................2x³ + 0x² + 8x

.....................................................3x + 7

Hence, (x⁵ + 6x³ + 11x + 7)/(x² + 4) = x³ + 2x + (3x + 7)/(x² + 4)

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