(6x⁴+20x²-4) / (x²+3)
(6x⁴+ 20x² -4) / (x²+3), Find a number that multiply by x² give the first expression 6x⁴, x² * 6x² = 6x⁴ and rule says that the sing have to change - to + or + to -, then continue the multipication quotient by divisor 6x²*3 = 18x² and appy the sing rule:
(6x⁴+ 20x² -4) / (x²+3)
-6x⁴ - 18x² ┃ 6x²
Continue the division until you get to something that the divisor is too big to divide into:
(6x⁴ - 6x⁴ ) + (20x² - 18x²) + 0 -4 / (x²+3)
0 + 2x² -4 / (x²+3)
-2x² - 6 ┃ 6x² +2
0 - 10
The binomial does not evenly divide into the ponomial, so the answer is
6x² +2 -(10/ (x²+3))