(3x⁴-5x³+x²+2)/(x²+3)
=(3x⁴+9x²-5x³-15x-8x²-24+15x+26)/(x²+3)
=[3x²(x²+3)-5x(x²+3)-8(x²+3)+15x+26)/(x²+3)
=3x²-5x-8 +(15x+26)/(x²+3)