How do you divide #(4a^4 -5a^2 +2a -10 )/(2a- 3)#?

1 Answer
Nov 1, 2016

The answer is #2a^3+3a^2+2a+4 +2/(2a-3)#

Explanation:

Let's make a long division
#color(white)(aaa)##4a^4##color(white)(aaaaa)##-5a^2+2a-10##∣##2a-3#
#color(white)(aaa)##4a^4-6a^3##color(white)(aaaaaaaaaaaaa)######2a^3+3a^2+2a+4#
#color(white)(aaaa)##0+6a^3-5a^2#
#color(white)(aaaaaa)##+6a^3-9a^2#
#color(white)(aaaaaaaaa)##0+4a^2+2a#
#color(white)(aaaaaaaaaaa)##+4a^2-6a#
#color(white)(aaaaaaaaaaaaaa)##0+8a-10#
#color(white)(aaaaaaaaaaaaaaaaaa)##8a-12#
#color(white)(aaaaaaaaaaaaaaaaaaaa)##0+2#

So the answer is #2a^3+3a^2+2a+4 +2/(2a-3)#